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

<!--XBRL Document Created with Wdesk from Workiva-->
<!--Copyright 2020 Workiva-->
<!--r:6a476640-2ca2-41e5-a859-142d1cf55b46,g:a2634207-952a-48db-8b2f-7461ea94616e-->
<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-20200731.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_b405182a-144a-432b-9509-ce878299ac95" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_CoverAbstract"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType_ec620d81-42e3-4ecf-9509-91d0438f78d1" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_DocumentType"/>
    <link:presentationArc order="1" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_b405182a-144a-432b-9509-ce878299ac95" xlink:to="loc_dei_DocumentType_ec620d81-42e3-4ecf-9509-91d0438f78d1" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate_ac2cfbd7-2d8f-4567-bd4b-fb62ce095e9e" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_DocumentPeriodEndDate"/>
    <link:presentationArc order="2" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_b405182a-144a-432b-9509-ce878299ac95" xlink:to="loc_dei_DocumentPeriodEndDate_ac2cfbd7-2d8f-4567-bd4b-fb62ce095e9e" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode_ec788725-daa2-4cba-91d3-2ce9437e922a" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:presentationArc order="3" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_b405182a-144a-432b-9509-ce878299ac95" xlink:to="loc_dei_EntityIncorporationStateCountryCode_ec788725-daa2-4cba-91d3-2ce9437e922a" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber_e1e39c88-ac4d-4282-bfa0-4636006f89fb" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityFileNumber"/>
    <link:presentationArc order="4" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_b405182a-144a-432b-9509-ce878299ac95" xlink:to="loc_dei_EntityFileNumber_e1e39c88-ac4d-4282-bfa0-4636006f89fb" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber_188e1603-59ca-4571-8e43-492f8ac1b8b7" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:presentationArc order="5" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_b405182a-144a-432b-9509-ce878299ac95" xlink:to="loc_dei_EntityTaxIdentificationNumber_188e1603-59ca-4571-8e43-492f8ac1b8b7" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1_ef088169-64c7-4059-b5b6-7e7b9c8ee902" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityAddressAddressLine1"/>
    <link:presentationArc order="6" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_b405182a-144a-432b-9509-ce878299ac95" xlink:to="loc_dei_EntityAddressAddressLine1_ef088169-64c7-4059-b5b6-7e7b9c8ee902" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown_906fb609-3849-4798-a2f8-a23ea2f45d9f" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityAddressCityOrTown"/>
    <link:presentationArc order="7" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_b405182a-144a-432b-9509-ce878299ac95" xlink:to="loc_dei_EntityAddressCityOrTown_906fb609-3849-4798-a2f8-a23ea2f45d9f" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode_ea3a2e31-d4de-4f8d-9d48-40fcc68c5124" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityAddressPostalZipCode"/>
    <link:presentationArc order="8" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_b405182a-144a-432b-9509-ce878299ac95" xlink:to="loc_dei_EntityAddressPostalZipCode_ea3a2e31-d4de-4f8d-9d48-40fcc68c5124" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCountry_0f2760c3-8c8d-45e7-b2f2-c6fb60dddaaa" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityAddressCountry"/>
    <link:presentationArc order="9" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_b405182a-144a-432b-9509-ce878299ac95" xlink:to="loc_dei_EntityAddressCountry_0f2760c3-8c8d-45e7-b2f2-c6fb60dddaaa" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CountryRegion_38f42705-8583-488e-bb1f-f0d8925df397" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_CountryRegion"/>
    <link:presentationArc order="10" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_b405182a-144a-432b-9509-ce878299ac95" xlink:to="loc_dei_CountryRegion_38f42705-8583-488e-bb1f-f0d8925df397" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode_efca5835-a619-4313-91b5-fdbcf65f9a24" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_CityAreaCode"/>
    <link:presentationArc order="11" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_b405182a-144a-432b-9509-ce878299ac95" xlink:to="loc_dei_CityAreaCode_efca5835-a619-4313-91b5-fdbcf65f9a24" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber_05d1dff1-a145-4ef3-b30e-f58c08237b21" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_LocalPhoneNumber"/>
    <link:presentationArc order="12" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_b405182a-144a-432b-9509-ce878299ac95" xlink:to="loc_dei_LocalPhoneNumber_05d1dff1-a145-4ef3-b30e-f58c08237b21" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_WrittenCommunications_f1a733f7-68cd-42f9-b93a-0b0dbe8de97d" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_WrittenCommunications"/>
    <link:presentationArc order="13" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_b405182a-144a-432b-9509-ce878299ac95" xlink:to="loc_dei_WrittenCommunications_f1a733f7-68cd-42f9-b93a-0b0dbe8de97d" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SolicitingMaterial_3ad5c3c0-9d96-466c-824a-275364b08f9e" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_SolicitingMaterial"/>
    <link:presentationArc order="14" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_b405182a-144a-432b-9509-ce878299ac95" xlink:to="loc_dei_SolicitingMaterial_3ad5c3c0-9d96-466c-824a-275364b08f9e" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementTenderOffer_9d596d68-3eed-468f-b28e-0d136931b731" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_PreCommencementTenderOffer"/>
    <link:presentationArc order="15" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_b405182a-144a-432b-9509-ce878299ac95" xlink:to="loc_dei_PreCommencementTenderOffer_9d596d68-3eed-468f-b28e-0d136931b731" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementIssuerTenderOffer_b54a8141-e4ce-4351-93b6-0e8c727a1ba8" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_PreCommencementIssuerTenderOffer"/>
    <link:presentationArc order="16" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_b405182a-144a-432b-9509-ce878299ac95" xlink:to="loc_dei_PreCommencementIssuerTenderOffer_b54a8141-e4ce-4351-93b6-0e8c727a1ba8" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle_2054bc2d-9e45-443d-baca-b2c24c27ba3a" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_Security12bTitle"/>
    <link:presentationArc order="17" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_b405182a-144a-432b-9509-ce878299ac95" xlink:to="loc_dei_Security12bTitle_2054bc2d-9e45-443d-baca-b2c24c27ba3a" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol_b091039e-ac2b-48ec-8954-90aa03ae042a" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_TradingSymbol"/>
    <link:presentationArc order="18" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_b405182a-144a-432b-9509-ce878299ac95" xlink:to="loc_dei_TradingSymbol_b091039e-ac2b-48ec-8954-90aa03ae042a" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName_da10fc27-87ed-4766-9a5b-56caf0904ed8" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_SecurityExchangeName"/>
    <link:presentationArc order="19" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_b405182a-144a-432b-9509-ce878299ac95" xlink:to="loc_dei_SecurityExchangeName_da10fc27-87ed-4766-9a5b-56caf0904ed8" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany_b951f880-ae70-44d5-b092-79c06ce9aa33" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:presentationArc order="20" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_b405182a-144a-432b-9509-ce878299ac95" xlink:to="loc_dei_EntityEmergingGrowthCompany_b951f880-ae70-44d5-b092-79c06ce9aa33" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName_47255540-42b4-454c-b258-c1638a6283f5" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityRegistrantName"/>
    <link:presentationArc order="21" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_b405182a-144a-432b-9509-ce878299ac95" xlink:to="loc_dei_EntityRegistrantName_47255540-42b4-454c-b258-c1638a6283f5" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey_49c629ab-1a03-4492-a586-1d9955cda2dd" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityCentralIndexKey"/>
    <link:presentationArc order="22" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_b405182a-144a-432b-9509-ce878299ac95" xlink:to="loc_dei_EntityCentralIndexKey_49c629ab-1a03-4492-a586-1d9955cda2dd" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag_bf4db1b1-e70c-4634-b783-62debaa5b05a" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_AmendmentFlag"/>
    <link:presentationArc order="23" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_b405182a-144a-432b-9509-ce878299ac95" xlink:to="loc_dei_AmendmentFlag_bf4db1b1-e70c-4634-b783-62debaa5b05a" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
  </link:presentationLink>
</link:linkbase>
