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

<!--XBRL Document Created with Wdesk from Workiva-->
<!--Copyright 2022 Workiva-->
<!--r:56558357-8960-417e-8eeb-42c3296edb5d,g:fb519105-d38d-4024-8c43-4c677ee2cd15-->
<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-20221212.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_111ca83b-6cc6-4a24-ac7e-925070773c84" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_CoverAbstract"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType_77aa1bad-7479-40ec-88ef-89957ee7daa5" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_DocumentType"/>
    <link:presentationArc order="1" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_111ca83b-6cc6-4a24-ac7e-925070773c84" xlink:to="loc_dei_DocumentType_77aa1bad-7479-40ec-88ef-89957ee7daa5" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate_3acf310c-421f-448f-8fc1-65705509544d" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_DocumentPeriodEndDate"/>
    <link:presentationArc order="2" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_111ca83b-6cc6-4a24-ac7e-925070773c84" xlink:to="loc_dei_DocumentPeriodEndDate_3acf310c-421f-448f-8fc1-65705509544d" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode_85b22c77-646f-40dc-9228-52baa47aeae9" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:presentationArc order="3" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_111ca83b-6cc6-4a24-ac7e-925070773c84" xlink:to="loc_dei_EntityIncorporationStateCountryCode_85b22c77-646f-40dc-9228-52baa47aeae9" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber_16d8483a-d0bd-4f78-a624-ec41b872345b" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_EntityFileNumber"/>
    <link:presentationArc order="4" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_111ca83b-6cc6-4a24-ac7e-925070773c84" xlink:to="loc_dei_EntityFileNumber_16d8483a-d0bd-4f78-a624-ec41b872345b" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber_462a0d64-12ca-4054-ae7d-513513f87ac2" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:presentationArc order="5" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_111ca83b-6cc6-4a24-ac7e-925070773c84" xlink:to="loc_dei_EntityTaxIdentificationNumber_462a0d64-12ca-4054-ae7d-513513f87ac2" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1_36cc6039-4783-4e5a-a97d-c58767b7d5cc" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_EntityAddressAddressLine1"/>
    <link:presentationArc order="6" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_111ca83b-6cc6-4a24-ac7e-925070773c84" xlink:to="loc_dei_EntityAddressAddressLine1_36cc6039-4783-4e5a-a97d-c58767b7d5cc" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown_bfde2efb-b232-429b-9ca3-6fed2f3430f9" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_EntityAddressCityOrTown"/>
    <link:presentationArc order="7" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_111ca83b-6cc6-4a24-ac7e-925070773c84" xlink:to="loc_dei_EntityAddressCityOrTown_bfde2efb-b232-429b-9ca3-6fed2f3430f9" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode_2bac032e-e132-452b-8659-d6f476de85e6" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_EntityAddressPostalZipCode"/>
    <link:presentationArc order="8" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_111ca83b-6cc6-4a24-ac7e-925070773c84" xlink:to="loc_dei_EntityAddressPostalZipCode_2bac032e-e132-452b-8659-d6f476de85e6" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCountry_ce14da2b-fb31-484c-82a9-661fbc4fab4e" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_EntityAddressCountry"/>
    <link:presentationArc order="9" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_111ca83b-6cc6-4a24-ac7e-925070773c84" xlink:to="loc_dei_EntityAddressCountry_ce14da2b-fb31-484c-82a9-661fbc4fab4e" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CountryRegion_bb2506a2-a3cb-4013-bfd9-922b02ce7a05" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_CountryRegion"/>
    <link:presentationArc order="10" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_111ca83b-6cc6-4a24-ac7e-925070773c84" xlink:to="loc_dei_CountryRegion_bb2506a2-a3cb-4013-bfd9-922b02ce7a05" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode_4b1e816e-6b4d-491d-99e3-c30ff9537734" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_CityAreaCode"/>
    <link:presentationArc order="11" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_111ca83b-6cc6-4a24-ac7e-925070773c84" xlink:to="loc_dei_CityAreaCode_4b1e816e-6b4d-491d-99e3-c30ff9537734" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber_1a0dcfd1-bacf-4cdc-bd00-760c3b97fa0e" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_LocalPhoneNumber"/>
    <link:presentationArc order="12" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_111ca83b-6cc6-4a24-ac7e-925070773c84" xlink:to="loc_dei_LocalPhoneNumber_1a0dcfd1-bacf-4cdc-bd00-760c3b97fa0e" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_WrittenCommunications_c42a06bd-03a6-4471-9f60-397e3c2e9591" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_WrittenCommunications"/>
    <link:presentationArc order="13" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_111ca83b-6cc6-4a24-ac7e-925070773c84" xlink:to="loc_dei_WrittenCommunications_c42a06bd-03a6-4471-9f60-397e3c2e9591" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SolicitingMaterial_4b6b8a24-dc56-4fbf-ab62-f0d064949195" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_SolicitingMaterial"/>
    <link:presentationArc order="14" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_111ca83b-6cc6-4a24-ac7e-925070773c84" xlink:to="loc_dei_SolicitingMaterial_4b6b8a24-dc56-4fbf-ab62-f0d064949195" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementTenderOffer_016b2013-c969-4e10-82e1-034f67f913af" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_PreCommencementTenderOffer"/>
    <link:presentationArc order="15" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_111ca83b-6cc6-4a24-ac7e-925070773c84" xlink:to="loc_dei_PreCommencementTenderOffer_016b2013-c969-4e10-82e1-034f67f913af" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementIssuerTenderOffer_54766b4c-9437-4705-9d2c-d3e3d01728f0" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_PreCommencementIssuerTenderOffer"/>
    <link:presentationArc order="16" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_111ca83b-6cc6-4a24-ac7e-925070773c84" xlink:to="loc_dei_PreCommencementIssuerTenderOffer_54766b4c-9437-4705-9d2c-d3e3d01728f0" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle_5437568f-8185-4ce2-8c27-a547f61d1e95" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_Security12bTitle"/>
    <link:presentationArc order="17" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_111ca83b-6cc6-4a24-ac7e-925070773c84" xlink:to="loc_dei_Security12bTitle_5437568f-8185-4ce2-8c27-a547f61d1e95" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol_5f00a973-24a7-4871-b0dc-2b63baf9eb30" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_TradingSymbol"/>
    <link:presentationArc order="18" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_111ca83b-6cc6-4a24-ac7e-925070773c84" xlink:to="loc_dei_TradingSymbol_5f00a973-24a7-4871-b0dc-2b63baf9eb30" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName_a126acb7-bec6-4dc5-96d1-ee6aa370e773" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_SecurityExchangeName"/>
    <link:presentationArc order="19" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_111ca83b-6cc6-4a24-ac7e-925070773c84" xlink:to="loc_dei_SecurityExchangeName_a126acb7-bec6-4dc5-96d1-ee6aa370e773" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany_16360924-a43d-4875-b062-1c7c5a6e5d80" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:presentationArc order="20" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_111ca83b-6cc6-4a24-ac7e-925070773c84" xlink:to="loc_dei_EntityEmergingGrowthCompany_16360924-a43d-4875-b062-1c7c5a6e5d80" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName_9c5c4bac-2063-4bbf-87aa-6ae0ac419894" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_EntityRegistrantName"/>
    <link:presentationArc order="21" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_111ca83b-6cc6-4a24-ac7e-925070773c84" xlink:to="loc_dei_EntityRegistrantName_9c5c4bac-2063-4bbf-87aa-6ae0ac419894" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey_0574df6a-0e76-4b17-856f-90da2c8b5da1" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_EntityCentralIndexKey"/>
    <link:presentationArc order="22" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_111ca83b-6cc6-4a24-ac7e-925070773c84" xlink:to="loc_dei_EntityCentralIndexKey_0574df6a-0e76-4b17-856f-90da2c8b5da1" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag_ea864551-d269-4050-a77c-9617313ff6e6" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_AmendmentFlag"/>
    <link:presentationArc order="23" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_111ca83b-6cc6-4a24-ac7e-925070773c84" xlink:to="loc_dei_AmendmentFlag_ea864551-d269-4050-a77c-9617313ff6e6" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
  </link:presentationLink>
</link:linkbase>
