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

<!--XBRL Document Created with Wdesk from Workiva-->
<!--Copyright 2023 Workiva-->
<!--r:dd3870b0-23b1-4961-bec9-31816964087f,g:6966e65c-b080-4384-a798-352c4cfce6ad-->
<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-20230217.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_280e71e8-3beb-4f19-a184-1dd8336e7b0d" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_CoverAbstract"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType_dff1c695-ce2a-4ee7-acce-4c485e9c2a43" 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_280e71e8-3beb-4f19-a184-1dd8336e7b0d" xlink:to="loc_dei_DocumentType_dff1c695-ce2a-4ee7-acce-4c485e9c2a43" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate_7fe1b218-5730-4e91-8b55-b81d0d711508" 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_280e71e8-3beb-4f19-a184-1dd8336e7b0d" xlink:to="loc_dei_DocumentPeriodEndDate_7fe1b218-5730-4e91-8b55-b81d0d711508" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode_6bee0326-cd8c-46fb-ae0c-425af75d91f1" 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_280e71e8-3beb-4f19-a184-1dd8336e7b0d" xlink:to="loc_dei_EntityIncorporationStateCountryCode_6bee0326-cd8c-46fb-ae0c-425af75d91f1" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber_ec96eef6-cdbb-4a00-b3c6-507629b0de21" 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_280e71e8-3beb-4f19-a184-1dd8336e7b0d" xlink:to="loc_dei_EntityFileNumber_ec96eef6-cdbb-4a00-b3c6-507629b0de21" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber_41213c13-af97-4811-89da-dff1cb1fbe8e" 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_280e71e8-3beb-4f19-a184-1dd8336e7b0d" xlink:to="loc_dei_EntityTaxIdentificationNumber_41213c13-af97-4811-89da-dff1cb1fbe8e" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1_e9ef576f-b73a-4ead-8f80-2fc14c5ca6da" 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_280e71e8-3beb-4f19-a184-1dd8336e7b0d" xlink:to="loc_dei_EntityAddressAddressLine1_e9ef576f-b73a-4ead-8f80-2fc14c5ca6da" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown_b4ad3532-873a-4498-a94a-9a57bcdfc79a" 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_280e71e8-3beb-4f19-a184-1dd8336e7b0d" xlink:to="loc_dei_EntityAddressCityOrTown_b4ad3532-873a-4498-a94a-9a57bcdfc79a" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode_4b9b9788-aaaf-4de0-bcb4-e88e86d349e6" 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_280e71e8-3beb-4f19-a184-1dd8336e7b0d" xlink:to="loc_dei_EntityAddressPostalZipCode_4b9b9788-aaaf-4de0-bcb4-e88e86d349e6" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCountry_29112563-a8e1-432c-8417-1f37d689b057" 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_280e71e8-3beb-4f19-a184-1dd8336e7b0d" xlink:to="loc_dei_EntityAddressCountry_29112563-a8e1-432c-8417-1f37d689b057" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CountryRegion_c8dafc4f-cb1f-41c2-9dac-e7a155565e41" 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_280e71e8-3beb-4f19-a184-1dd8336e7b0d" xlink:to="loc_dei_CountryRegion_c8dafc4f-cb1f-41c2-9dac-e7a155565e41" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode_da591307-8f9d-43ce-bb1d-652181da502c" 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_280e71e8-3beb-4f19-a184-1dd8336e7b0d" xlink:to="loc_dei_CityAreaCode_da591307-8f9d-43ce-bb1d-652181da502c" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber_42a4fb58-3d55-45f0-ba2f-832a6d1fff47" 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_280e71e8-3beb-4f19-a184-1dd8336e7b0d" xlink:to="loc_dei_LocalPhoneNumber_42a4fb58-3d55-45f0-ba2f-832a6d1fff47" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_WrittenCommunications_304ea6a9-0584-4689-93ec-f5dbf689b678" 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_280e71e8-3beb-4f19-a184-1dd8336e7b0d" xlink:to="loc_dei_WrittenCommunications_304ea6a9-0584-4689-93ec-f5dbf689b678" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SolicitingMaterial_7dc52336-8990-4501-a8dd-a594280195be" 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_280e71e8-3beb-4f19-a184-1dd8336e7b0d" xlink:to="loc_dei_SolicitingMaterial_7dc52336-8990-4501-a8dd-a594280195be" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementTenderOffer_68ac26f5-5ac1-480a-a68a-9d6863721213" 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_280e71e8-3beb-4f19-a184-1dd8336e7b0d" xlink:to="loc_dei_PreCommencementTenderOffer_68ac26f5-5ac1-480a-a68a-9d6863721213" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementIssuerTenderOffer_d9c79111-8ff7-4b30-9898-8b228bd900dc" 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_280e71e8-3beb-4f19-a184-1dd8336e7b0d" xlink:to="loc_dei_PreCommencementIssuerTenderOffer_d9c79111-8ff7-4b30-9898-8b228bd900dc" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle_60fe56c0-bb91-454c-b638-d029967f0bea" 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_280e71e8-3beb-4f19-a184-1dd8336e7b0d" xlink:to="loc_dei_Security12bTitle_60fe56c0-bb91-454c-b638-d029967f0bea" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol_ec7d0df8-4b94-4d65-808f-31f53fc2dced" 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_280e71e8-3beb-4f19-a184-1dd8336e7b0d" xlink:to="loc_dei_TradingSymbol_ec7d0df8-4b94-4d65-808f-31f53fc2dced" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName_e064f2ca-ef1f-40dd-b43b-13e9fc752cda" 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_280e71e8-3beb-4f19-a184-1dd8336e7b0d" xlink:to="loc_dei_SecurityExchangeName_e064f2ca-ef1f-40dd-b43b-13e9fc752cda" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany_3aa45f86-a5e7-49ad-b4b8-23791e5a8adc" 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_280e71e8-3beb-4f19-a184-1dd8336e7b0d" xlink:to="loc_dei_EntityEmergingGrowthCompany_3aa45f86-a5e7-49ad-b4b8-23791e5a8adc" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName_34699745-9a03-426a-9b42-d76c9b1cfe0a" 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_280e71e8-3beb-4f19-a184-1dd8336e7b0d" xlink:to="loc_dei_EntityRegistrantName_34699745-9a03-426a-9b42-d76c9b1cfe0a" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey_ac80707f-ba36-41a9-984e-bb07dee1b126" 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_280e71e8-3beb-4f19-a184-1dd8336e7b0d" xlink:to="loc_dei_EntityCentralIndexKey_ac80707f-ba36-41a9-984e-bb07dee1b126" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag_e62646d5-54c2-4bf7-b18d-b8b51bcbeae1" 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_280e71e8-3beb-4f19-a184-1dd8336e7b0d" xlink:to="loc_dei_AmendmentFlag_e62646d5-54c2-4bf7-b18d-b8b51bcbeae1" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
  </link:presentationLink>
</link:linkbase>
