<?xml version="1.0" encoding="UTF-8"?>

<!--XBRL Document Created with Wdesk from Workiva-->
<!--Copyright 2021 Workiva-->
<!--r:fc760aaa-1dd5-433c-b60b-e46a3283d196,g:51c2c937-c344-4df3-96ab-2d0d39ff3f56-->
<link:linkbase xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd">
  <link:roleRef roleURI="http://www.livanova.cyberonics.com/role/DocumentandEntityInformationDocument" xlink:type="simple" xlink:href="livn-20211112.xsd#DocumentandEntityInformationDocument"/>
  <link:presentationLink xlink:role="http://www.livanova.cyberonics.com/role/DocumentandEntityInformationDocument" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract_732f21f8-12bb-4bb0-842f-c7d64f3afde6" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_CoverAbstract"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType_2f40b24f-fbe0-4330-8af6-19565d8414ee" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_DocumentType"/>
    <link:presentationArc order="1" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_732f21f8-12bb-4bb0-842f-c7d64f3afde6" xlink:to="loc_dei_DocumentType_2f40b24f-fbe0-4330-8af6-19565d8414ee" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate_d3fcb95e-a132-43e6-ac1d-a84093eca5f1" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_DocumentPeriodEndDate"/>
    <link:presentationArc order="2" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_732f21f8-12bb-4bb0-842f-c7d64f3afde6" xlink:to="loc_dei_DocumentPeriodEndDate_d3fcb95e-a132-43e6-ac1d-a84093eca5f1" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode_69bb07eb-c3b0-4c3e-8ab7-2846e477c62e" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:presentationArc order="3" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_732f21f8-12bb-4bb0-842f-c7d64f3afde6" xlink:to="loc_dei_EntityIncorporationStateCountryCode_69bb07eb-c3b0-4c3e-8ab7-2846e477c62e" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber_d95aa570-aa2a-4236-8290-28a3b69e0c02" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntityFileNumber"/>
    <link:presentationArc order="4" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_732f21f8-12bb-4bb0-842f-c7d64f3afde6" xlink:to="loc_dei_EntityFileNumber_d95aa570-aa2a-4236-8290-28a3b69e0c02" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber_6bb50fa9-c952-4ba3-a6c9-ce32294fda82" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:presentationArc order="5" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_732f21f8-12bb-4bb0-842f-c7d64f3afde6" xlink:to="loc_dei_EntityTaxIdentificationNumber_6bb50fa9-c952-4ba3-a6c9-ce32294fda82" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1_64cac7e4-2050-4c26-be8c-8fae14c5cb34" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntityAddressAddressLine1"/>
    <link:presentationArc order="6" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_732f21f8-12bb-4bb0-842f-c7d64f3afde6" xlink:to="loc_dei_EntityAddressAddressLine1_64cac7e4-2050-4c26-be8c-8fae14c5cb34" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown_1c810283-1dde-4d2f-afcc-975d177ecb7c" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntityAddressCityOrTown"/>
    <link:presentationArc order="7" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_732f21f8-12bb-4bb0-842f-c7d64f3afde6" xlink:to="loc_dei_EntityAddressCityOrTown_1c810283-1dde-4d2f-afcc-975d177ecb7c" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode_3bd6ac1c-6579-428e-8738-16629673ca1f" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntityAddressPostalZipCode"/>
    <link:presentationArc order="8" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_732f21f8-12bb-4bb0-842f-c7d64f3afde6" xlink:to="loc_dei_EntityAddressPostalZipCode_3bd6ac1c-6579-428e-8738-16629673ca1f" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCountry_14d8e4a1-3c89-499b-8f5e-c9e23c1365c2" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntityAddressCountry"/>
    <link:presentationArc order="9" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_732f21f8-12bb-4bb0-842f-c7d64f3afde6" xlink:to="loc_dei_EntityAddressCountry_14d8e4a1-3c89-499b-8f5e-c9e23c1365c2" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CountryRegion_718e8e0f-fe19-4def-a248-5748cfc91021" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_CountryRegion"/>
    <link:presentationArc order="10" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_732f21f8-12bb-4bb0-842f-c7d64f3afde6" xlink:to="loc_dei_CountryRegion_718e8e0f-fe19-4def-a248-5748cfc91021" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode_7ccde3da-37e6-4ba3-b312-58d22f38fb7d" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_CityAreaCode"/>
    <link:presentationArc order="11" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_732f21f8-12bb-4bb0-842f-c7d64f3afde6" xlink:to="loc_dei_CityAreaCode_7ccde3da-37e6-4ba3-b312-58d22f38fb7d" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber_cdb9daa8-9a4b-431d-abc2-4b056814c1ea" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_LocalPhoneNumber"/>
    <link:presentationArc order="12" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_732f21f8-12bb-4bb0-842f-c7d64f3afde6" xlink:to="loc_dei_LocalPhoneNumber_cdb9daa8-9a4b-431d-abc2-4b056814c1ea" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_WrittenCommunications_bedf30c6-4d5d-4e42-98a7-d481b65181a6" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_WrittenCommunications"/>
    <link:presentationArc order="13" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_732f21f8-12bb-4bb0-842f-c7d64f3afde6" xlink:to="loc_dei_WrittenCommunications_bedf30c6-4d5d-4e42-98a7-d481b65181a6" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SolicitingMaterial_c8733dfd-7b0b-45c9-9df9-9f208aa0ecd7" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_SolicitingMaterial"/>
    <link:presentationArc order="14" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_732f21f8-12bb-4bb0-842f-c7d64f3afde6" xlink:to="loc_dei_SolicitingMaterial_c8733dfd-7b0b-45c9-9df9-9f208aa0ecd7" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementTenderOffer_49e476fb-b431-4467-8dfd-2c302dfa5a38" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_PreCommencementTenderOffer"/>
    <link:presentationArc order="15" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_732f21f8-12bb-4bb0-842f-c7d64f3afde6" xlink:to="loc_dei_PreCommencementTenderOffer_49e476fb-b431-4467-8dfd-2c302dfa5a38" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementIssuerTenderOffer_2344b54d-45d8-4ffc-b540-374527504d1d" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_PreCommencementIssuerTenderOffer"/>
    <link:presentationArc order="16" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_732f21f8-12bb-4bb0-842f-c7d64f3afde6" xlink:to="loc_dei_PreCommencementIssuerTenderOffer_2344b54d-45d8-4ffc-b540-374527504d1d" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle_c56f3fb6-c07d-4760-9e08-643bb8e7a432" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_Security12bTitle"/>
    <link:presentationArc order="17" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_732f21f8-12bb-4bb0-842f-c7d64f3afde6" xlink:to="loc_dei_Security12bTitle_c56f3fb6-c07d-4760-9e08-643bb8e7a432" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol_246da4c8-657c-42e8-a101-7a24615168c9" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_TradingSymbol"/>
    <link:presentationArc order="18" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_732f21f8-12bb-4bb0-842f-c7d64f3afde6" xlink:to="loc_dei_TradingSymbol_246da4c8-657c-42e8-a101-7a24615168c9" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName_1c3251c0-1acd-422f-8d2c-705052a1398b" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_SecurityExchangeName"/>
    <link:presentationArc order="19" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_732f21f8-12bb-4bb0-842f-c7d64f3afde6" xlink:to="loc_dei_SecurityExchangeName_1c3251c0-1acd-422f-8d2c-705052a1398b" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany_e2beb531-74f6-4bb2-83d2-c233612ef923" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:presentationArc order="20" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_732f21f8-12bb-4bb0-842f-c7d64f3afde6" xlink:to="loc_dei_EntityEmergingGrowthCompany_e2beb531-74f6-4bb2-83d2-c233612ef923" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName_20fa0bac-5635-4102-a7bd-170e283690fe" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntityRegistrantName"/>
    <link:presentationArc order="21" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_732f21f8-12bb-4bb0-842f-c7d64f3afde6" xlink:to="loc_dei_EntityRegistrantName_20fa0bac-5635-4102-a7bd-170e283690fe" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey_1868e35f-125a-4b57-be72-55e536b1c0ee" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_EntityCentralIndexKey"/>
    <link:presentationArc order="22" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_732f21f8-12bb-4bb0-842f-c7d64f3afde6" xlink:to="loc_dei_EntityCentralIndexKey_1868e35f-125a-4b57-be72-55e536b1c0ee" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag_30457546-e7b6-4c9f-9684-b89d5751daf3" xlink:href="https://xbrl.sec.gov/dei/2020/dei-2020-01-31.xsd#dei_AmendmentFlag"/>
    <link:presentationArc order="23" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_732f21f8-12bb-4bb0-842f-c7d64f3afde6" xlink:to="loc_dei_AmendmentFlag_30457546-e7b6-4c9f-9684-b89d5751daf3" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
  </link:presentationLink>
</link:linkbase>
