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

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2026 Workiva-->
<!--r:019d16a9-9e84-7794-9387-47e5bac0c587,g:268421b2-c3d2-4bc0-9d5a-5328ea0eca3e-->
<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" xmlns:xbrldt="http://xbrl.org/2005/xbrldt" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd">
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/all" xlink:type="simple" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#all"/>
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:type="simple" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#hypercube-dimension"/>
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:type="simple" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#dimension-default"/>
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:type="simple" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#dimension-domain"/>
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/domain-member" xlink:type="simple" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#domain-member"/>
  <link:roleRef roleURI="http://www.archcapgroup.com/role/DocumentandEntityInformationCover" xlink:type="simple" xlink:href="acgl-20260602.xsd#DocumentandEntityInformationCover"/>
  <link:definitionLink xlink:role="http://www.archcapgroup.com/role/DocumentandEntityInformationCover" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityListingsLineItems_019d16a9-9e84-7c69-8c10-849a9b1d079a" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityListingsLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityListingsTable_019d16a9-9e84-739e-bce5-6c87fc52a745" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityListingsTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_dei_EntityListingsLineItems_019d16a9-9e84-7c69-8c10-849a9b1d079a" xlink:to="loc_dei_EntityListingsTable_019d16a9-9e84-739e-bce5-6c87fc52a745" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementClassOfStockAxis_019d16a9-9e84-7d85-b1f9-fd91efd47235" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementClassOfStockAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_dei_EntityListingsTable_019d16a9-9e84-739e-bce5-6c87fc52a745" xlink:to="loc_us-gaap_StatementClassOfStockAxis_019d16a9-9e84-7d85-b1f9-fd91efd47235" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain_019d16a9-9e84-7d85-b1f9-fd91efd47235_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfStockDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementClassOfStockAxis_019d16a9-9e84-7d85-b1f9-fd91efd47235" xlink:to="loc_us-gaap_ClassOfStockDomain_019d16a9-9e84-7d85-b1f9-fd91efd47235_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain_019d16a9-9e84-7758-99b7-23593159f9d9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfStockDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementClassOfStockAxis_019d16a9-9e84-7d85-b1f9-fd91efd47235" xlink:to="loc_us-gaap_ClassOfStockDomain_019d16a9-9e84-7758-99b7-23593159f9d9" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember_019d16a9-9e84-7971-9183-0a428d8a7d0b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockDomain_019d16a9-9e84-7758-99b7-23593159f9d9" xlink:to="loc_us-gaap_CommonStockMember_019d16a9-9e84-7971-9183-0a428d8a7d0b" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_acgl_SeriesFDepositaryShareEquivalentMember_019d16a9-9e84-7693-a4e2-d4d0350430b6" xlink:href="acgl-20260602.xsd#acgl_SeriesFDepositaryShareEquivalentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockDomain_019d16a9-9e84-7758-99b7-23593159f9d9" xlink:to="loc_acgl_SeriesFDepositaryShareEquivalentMember_019d16a9-9e84-7693-a4e2-d4d0350430b6" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_acgl_SeriesGDepositaryShareEquivalentMember_019d16a9-9e84-7d66-8225-02d761539ecf" xlink:href="acgl-20260602.xsd#acgl_SeriesGDepositaryShareEquivalentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockDomain_019d16a9-9e84-7758-99b7-23593159f9d9" xlink:to="loc_acgl_SeriesGDepositaryShareEquivalentMember_019d16a9-9e84-7d66-8225-02d761539ecf" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle_019d16a9-9e84-7225-83eb-67a5abc1a26c" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_Security12bTitle"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_dei_EntityListingsLineItems_019d16a9-9e84-7c69-8c10-849a9b1d079a" xlink:to="loc_dei_Security12bTitle_019d16a9-9e84-7225-83eb-67a5abc1a26c" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol_019d16a9-9e84-77a9-86a7-f3a2a988aa83" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_TradingSymbol"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_dei_EntityListingsLineItems_019d16a9-9e84-7c69-8c10-849a9b1d079a" xlink:to="loc_dei_TradingSymbol_019d16a9-9e84-77a9-86a7-f3a2a988aa83" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName_019d16a9-9e84-776c-8569-50f48249c933" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_SecurityExchangeName"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_dei_EntityListingsLineItems_019d16a9-9e84-7c69-8c10-849a9b1d079a" xlink:to="loc_dei_SecurityExchangeName_019d16a9-9e84-776c-8569-50f48249c933" xlink:type="arc" order="2"/>
  </link:definitionLink>
</link:linkbase>
