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

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2023 Workiva-->
<!--r:c0d7ecb6-2931-4842-b9ce-af51c9639ba1,g:a0b6b73e-527d-450a-9202-c6e40cbb57ff-->
<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-20231019.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_ab6f7bfc-a8a9-4b4e-aae3-655e97f34e61" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_CoverAbstract"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType_345a9d33-c186-4583-8952-e320cd46292c" 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_ab6f7bfc-a8a9-4b4e-aae3-655e97f34e61" xlink:to="loc_dei_DocumentType_345a9d33-c186-4583-8952-e320cd46292c" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate_9495d7de-878b-4a8c-9aa4-047b629d3160" 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_ab6f7bfc-a8a9-4b4e-aae3-655e97f34e61" xlink:to="loc_dei_DocumentPeriodEndDate_9495d7de-878b-4a8c-9aa4-047b629d3160" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode_35bc8cbb-6697-47c4-afab-4cb1b21f3f1b" 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_ab6f7bfc-a8a9-4b4e-aae3-655e97f34e61" xlink:to="loc_dei_EntityIncorporationStateCountryCode_35bc8cbb-6697-47c4-afab-4cb1b21f3f1b" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber_73369419-126e-4c85-a4f2-4ebe27a13868" 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_ab6f7bfc-a8a9-4b4e-aae3-655e97f34e61" xlink:to="loc_dei_EntityFileNumber_73369419-126e-4c85-a4f2-4ebe27a13868" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber_e5a4b863-8811-489b-9c2e-30029c273b4d" 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_ab6f7bfc-a8a9-4b4e-aae3-655e97f34e61" xlink:to="loc_dei_EntityTaxIdentificationNumber_e5a4b863-8811-489b-9c2e-30029c273b4d" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1_83d090d0-7c8f-45e3-82c3-7a6db1214d08" 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_ab6f7bfc-a8a9-4b4e-aae3-655e97f34e61" xlink:to="loc_dei_EntityAddressAddressLine1_83d090d0-7c8f-45e3-82c3-7a6db1214d08" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown_65fcaba4-ff9c-4bb3-88c3-39151eb9d962" 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_ab6f7bfc-a8a9-4b4e-aae3-655e97f34e61" xlink:to="loc_dei_EntityAddressCityOrTown_65fcaba4-ff9c-4bb3-88c3-39151eb9d962" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode_a94c7a5b-c58c-453b-b411-e8e25a66fc1b" 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_ab6f7bfc-a8a9-4b4e-aae3-655e97f34e61" xlink:to="loc_dei_EntityAddressPostalZipCode_a94c7a5b-c58c-453b-b411-e8e25a66fc1b" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCountry_17e0c0e2-9033-46ea-a1b8-ad43f5cd5a14" 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_ab6f7bfc-a8a9-4b4e-aae3-655e97f34e61" xlink:to="loc_dei_EntityAddressCountry_17e0c0e2-9033-46ea-a1b8-ad43f5cd5a14" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CountryRegion_a22163cd-f296-4cff-bfef-9a7d20c0c70a" 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_ab6f7bfc-a8a9-4b4e-aae3-655e97f34e61" xlink:to="loc_dei_CountryRegion_a22163cd-f296-4cff-bfef-9a7d20c0c70a" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode_f130eff0-cfb8-450e-b924-282f4350d87d" 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_ab6f7bfc-a8a9-4b4e-aae3-655e97f34e61" xlink:to="loc_dei_CityAreaCode_f130eff0-cfb8-450e-b924-282f4350d87d" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber_0ca9c36a-9979-4009-84ca-5cf919e3713e" 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_ab6f7bfc-a8a9-4b4e-aae3-655e97f34e61" xlink:to="loc_dei_LocalPhoneNumber_0ca9c36a-9979-4009-84ca-5cf919e3713e" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_WrittenCommunications_703927c5-a97b-428d-b45c-dc22552fedf5" 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_ab6f7bfc-a8a9-4b4e-aae3-655e97f34e61" xlink:to="loc_dei_WrittenCommunications_703927c5-a97b-428d-b45c-dc22552fedf5" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SolicitingMaterial_cb36bbe5-7287-43d4-9479-812c0f912188" 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_ab6f7bfc-a8a9-4b4e-aae3-655e97f34e61" xlink:to="loc_dei_SolicitingMaterial_cb36bbe5-7287-43d4-9479-812c0f912188" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementTenderOffer_98a62f87-be09-45b3-930e-4e4e8aa05399" 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_ab6f7bfc-a8a9-4b4e-aae3-655e97f34e61" xlink:to="loc_dei_PreCommencementTenderOffer_98a62f87-be09-45b3-930e-4e4e8aa05399" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementIssuerTenderOffer_4c2595c4-dbb9-4bf9-b2ad-05a7648e901d" 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_ab6f7bfc-a8a9-4b4e-aae3-655e97f34e61" xlink:to="loc_dei_PreCommencementIssuerTenderOffer_4c2595c4-dbb9-4bf9-b2ad-05a7648e901d" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle_bf77e7c6-3843-46fb-a2a4-c103d62f245d" 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_ab6f7bfc-a8a9-4b4e-aae3-655e97f34e61" xlink:to="loc_dei_Security12bTitle_bf77e7c6-3843-46fb-a2a4-c103d62f245d" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol_feb315a3-894c-427b-a04e-210bc83f04cf" 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_ab6f7bfc-a8a9-4b4e-aae3-655e97f34e61" xlink:to="loc_dei_TradingSymbol_feb315a3-894c-427b-a04e-210bc83f04cf" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName_6193930d-ba63-431a-ba95-73dcc4bd3f2f" 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_ab6f7bfc-a8a9-4b4e-aae3-655e97f34e61" xlink:to="loc_dei_SecurityExchangeName_6193930d-ba63-431a-ba95-73dcc4bd3f2f" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany_ad81c15f-52ca-4d58-85d2-e3436dda8069" 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_ab6f7bfc-a8a9-4b4e-aae3-655e97f34e61" xlink:to="loc_dei_EntityEmergingGrowthCompany_ad81c15f-52ca-4d58-85d2-e3436dda8069" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName_9b5341a5-d7d6-4915-a277-216937a8e120" 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_ab6f7bfc-a8a9-4b4e-aae3-655e97f34e61" xlink:to="loc_dei_EntityRegistrantName_9b5341a5-d7d6-4915-a277-216937a8e120" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey_5d119599-02f4-4e1b-9560-e776e1a863b4" 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_ab6f7bfc-a8a9-4b4e-aae3-655e97f34e61" xlink:to="loc_dei_EntityCentralIndexKey_5d119599-02f4-4e1b-9560-e776e1a863b4" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag_8a20d15c-acbf-4be9-95e6-5f83149c0c95" 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_ab6f7bfc-a8a9-4b4e-aae3-655e97f34e61" xlink:to="loc_dei_AmendmentFlag_8a20d15c-acbf-4be9-95e6-5f83149c0c95" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
  </link:presentationLink>
</link:linkbase>
