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

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2023 Workiva-->
<!--r:d984beb0-5466-4baa-ae43-5b39fa8f3bd4,g:8c01b572-7eba-4514-b863-07c35bdd19e3-->
<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-20230726.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_5e1d4af2-a9c5-4681-9988-f72403d21da1" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_CoverAbstract"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType_ce6023c6-e55d-499b-9e84-dabe877fb505" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentType"/>
    <link:presentationArc order="1" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_5e1d4af2-a9c5-4681-9988-f72403d21da1" xlink:to="loc_dei_DocumentType_ce6023c6-e55d-499b-9e84-dabe877fb505" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate_3c2c37a2-e56b-45ab-bfde-b23330225810" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentPeriodEndDate"/>
    <link:presentationArc order="2" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_5e1d4af2-a9c5-4681-9988-f72403d21da1" xlink:to="loc_dei_DocumentPeriodEndDate_3c2c37a2-e56b-45ab-bfde-b23330225810" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode_05c926e0-1481-4dad-aed7-09279b61cb58" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:presentationArc order="3" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_5e1d4af2-a9c5-4681-9988-f72403d21da1" xlink:to="loc_dei_EntityIncorporationStateCountryCode_05c926e0-1481-4dad-aed7-09279b61cb58" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber_92661967-0c61-44cc-be02-3345819deec7" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityFileNumber"/>
    <link:presentationArc order="4" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_5e1d4af2-a9c5-4681-9988-f72403d21da1" xlink:to="loc_dei_EntityFileNumber_92661967-0c61-44cc-be02-3345819deec7" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber_b135a994-b631-454a-a40d-decd843f581a" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:presentationArc order="5" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_5e1d4af2-a9c5-4681-9988-f72403d21da1" xlink:to="loc_dei_EntityTaxIdentificationNumber_b135a994-b631-454a-a40d-decd843f581a" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1_2fd5501b-eb60-492d-9d91-cb3066169d44" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressAddressLine1"/>
    <link:presentationArc order="6" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_5e1d4af2-a9c5-4681-9988-f72403d21da1" xlink:to="loc_dei_EntityAddressAddressLine1_2fd5501b-eb60-492d-9d91-cb3066169d44" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown_45c0baa1-768d-4a41-8e67-dc487cdca5c7" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressCityOrTown"/>
    <link:presentationArc order="7" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_5e1d4af2-a9c5-4681-9988-f72403d21da1" xlink:to="loc_dei_EntityAddressCityOrTown_45c0baa1-768d-4a41-8e67-dc487cdca5c7" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode_bfa2bb60-6eaa-4238-bf90-517fdbc01c04" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressPostalZipCode"/>
    <link:presentationArc order="8" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_5e1d4af2-a9c5-4681-9988-f72403d21da1" xlink:to="loc_dei_EntityAddressPostalZipCode_bfa2bb60-6eaa-4238-bf90-517fdbc01c04" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCountry_0c5b131e-8deb-408b-83ff-0605fbd96eef" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressCountry"/>
    <link:presentationArc order="9" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_5e1d4af2-a9c5-4681-9988-f72403d21da1" xlink:to="loc_dei_EntityAddressCountry_0c5b131e-8deb-408b-83ff-0605fbd96eef" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CountryRegion_94318db1-7443-4d52-a61c-ca84fe701323" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_CountryRegion"/>
    <link:presentationArc order="10" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_5e1d4af2-a9c5-4681-9988-f72403d21da1" xlink:to="loc_dei_CountryRegion_94318db1-7443-4d52-a61c-ca84fe701323" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode_ca8a66aa-89f0-4aa8-816a-232a4eb0d3c2" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_CityAreaCode"/>
    <link:presentationArc order="11" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_5e1d4af2-a9c5-4681-9988-f72403d21da1" xlink:to="loc_dei_CityAreaCode_ca8a66aa-89f0-4aa8-816a-232a4eb0d3c2" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber_fb6f892c-9d43-4258-914b-2e87bb153fcf" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_LocalPhoneNumber"/>
    <link:presentationArc order="12" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_5e1d4af2-a9c5-4681-9988-f72403d21da1" xlink:to="loc_dei_LocalPhoneNumber_fb6f892c-9d43-4258-914b-2e87bb153fcf" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_WrittenCommunications_ebd30c94-ee4c-48e9-8c3a-ea6b2bdebd1e" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_WrittenCommunications"/>
    <link:presentationArc order="13" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_5e1d4af2-a9c5-4681-9988-f72403d21da1" xlink:to="loc_dei_WrittenCommunications_ebd30c94-ee4c-48e9-8c3a-ea6b2bdebd1e" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SolicitingMaterial_bc222d0c-937e-48d7-b284-6b6749a80191" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_SolicitingMaterial"/>
    <link:presentationArc order="14" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_5e1d4af2-a9c5-4681-9988-f72403d21da1" xlink:to="loc_dei_SolicitingMaterial_bc222d0c-937e-48d7-b284-6b6749a80191" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementTenderOffer_5e0d797a-b3fe-40d1-bfdd-0ed0ea6a0f19" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_PreCommencementTenderOffer"/>
    <link:presentationArc order="15" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_5e1d4af2-a9c5-4681-9988-f72403d21da1" xlink:to="loc_dei_PreCommencementTenderOffer_5e0d797a-b3fe-40d1-bfdd-0ed0ea6a0f19" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementIssuerTenderOffer_db4a5586-8118-4345-8f20-ec0e9db1c0e8" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_PreCommencementIssuerTenderOffer"/>
    <link:presentationArc order="16" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_5e1d4af2-a9c5-4681-9988-f72403d21da1" xlink:to="loc_dei_PreCommencementIssuerTenderOffer_db4a5586-8118-4345-8f20-ec0e9db1c0e8" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle_656c645b-b522-4281-ba8b-6825b893bedc" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_Security12bTitle"/>
    <link:presentationArc order="17" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_5e1d4af2-a9c5-4681-9988-f72403d21da1" xlink:to="loc_dei_Security12bTitle_656c645b-b522-4281-ba8b-6825b893bedc" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol_2269f990-9202-4477-815b-14a9efe0db0b" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_TradingSymbol"/>
    <link:presentationArc order="18" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_5e1d4af2-a9c5-4681-9988-f72403d21da1" xlink:to="loc_dei_TradingSymbol_2269f990-9202-4477-815b-14a9efe0db0b" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName_5bd825f4-0386-4a75-8ce5-4578a8c09497" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_SecurityExchangeName"/>
    <link:presentationArc order="19" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_5e1d4af2-a9c5-4681-9988-f72403d21da1" xlink:to="loc_dei_SecurityExchangeName_5bd825f4-0386-4a75-8ce5-4578a8c09497" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany_18197b5e-addc-4541-9b94-7bc56ed0404c" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:presentationArc order="20" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_5e1d4af2-a9c5-4681-9988-f72403d21da1" xlink:to="loc_dei_EntityEmergingGrowthCompany_18197b5e-addc-4541-9b94-7bc56ed0404c" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName_278ce4be-1c9d-4215-84d0-8bf13aad1655" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityRegistrantName"/>
    <link:presentationArc order="21" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_5e1d4af2-a9c5-4681-9988-f72403d21da1" xlink:to="loc_dei_EntityRegistrantName_278ce4be-1c9d-4215-84d0-8bf13aad1655" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey_19728247-fe55-4ca9-8813-26e96a78fad6" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityCentralIndexKey"/>
    <link:presentationArc order="22" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_5e1d4af2-a9c5-4681-9988-f72403d21da1" xlink:to="loc_dei_EntityCentralIndexKey_19728247-fe55-4ca9-8813-26e96a78fad6" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag_63f2b166-dd15-4a04-861b-0df57f9dc837" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_AmendmentFlag"/>
    <link:presentationArc order="23" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_5e1d4af2-a9c5-4681-9988-f72403d21da1" xlink:to="loc_dei_AmendmentFlag_63f2b166-dd15-4a04-861b-0df57f9dc837" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
  </link:presentationLink>
</link:linkbase>
