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

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2026 Workiva-->
<!--r:01a18db9-d326-7376-b9f4-09a702e488bc,g:1ce1be68-6dbc-42f2-abdd-2234e991df01-->
<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-20261030.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_01a18db9-d326-7442-89b9-b1dfc745e0fb" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityListingsLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityListingsTable_01a18db9-d326-7ead-955c-c6b40cb6fb21" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityListingsTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_dei_EntityListingsLineItems_01a18db9-d326-7442-89b9-b1dfc745e0fb" xlink:to="loc_dei_EntityListingsTable_01a18db9-d326-7ead-955c-c6b40cb6fb21" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementClassOfStockAxis_01a18db9-d326-7a5f-ac4a-fe4bdf24a77e" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementClassOfStockAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_dei_EntityListingsTable_01a18db9-d326-7ead-955c-c6b40cb6fb21" xlink:to="loc_us-gaap_StatementClassOfStockAxis_01a18db9-d326-7a5f-ac4a-fe4bdf24a77e" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain_01a18db9-d326-7a5f-ac4a-fe4bdf24a77e_default" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementClassOfStockAxis_01a18db9-d326-7a5f-ac4a-fe4bdf24a77e" xlink:to="loc_us-gaap_ClassOfStockDomain_01a18db9-d326-7a5f-ac4a-fe4bdf24a77e_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain_01a18db9-d326-72d7-8bb9-01100b1844f3" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementClassOfStockAxis_01a18db9-d326-7a5f-ac4a-fe4bdf24a77e" xlink:to="loc_us-gaap_ClassOfStockDomain_01a18db9-d326-72d7-8bb9-01100b1844f3" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember_01a18db9-d326-75e3-ac1e-ad2ffd848b81" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockDomain_01a18db9-d326-72d7-8bb9-01100b1844f3" xlink:to="loc_us-gaap_CommonStockMember_01a18db9-d326-75e3-ac1e-ad2ffd848b81" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_acgl_SeriesFDepositaryShareEquivalentMember_01a18db9-d326-7e97-8968-e9d35d0fea1b" xlink:href="acgl-20261030.xsd#acgl_SeriesFDepositaryShareEquivalentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockDomain_01a18db9-d326-72d7-8bb9-01100b1844f3" xlink:to="loc_acgl_SeriesFDepositaryShareEquivalentMember_01a18db9-d326-7e97-8968-e9d35d0fea1b" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_acgl_SeriesGDepositaryShareEquivalentMember_01a18db9-d326-7b95-b72c-79683a73476d" xlink:href="acgl-20261030.xsd#acgl_SeriesGDepositaryShareEquivalentMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockDomain_01a18db9-d326-72d7-8bb9-01100b1844f3" xlink:to="loc_acgl_SeriesGDepositaryShareEquivalentMember_01a18db9-d326-7b95-b72c-79683a73476d" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle_01a18db9-d326-7c03-8efd-198d9b0c267e" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_Security12bTitle"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_dei_EntityListingsLineItems_01a18db9-d326-7442-89b9-b1dfc745e0fb" xlink:to="loc_dei_Security12bTitle_01a18db9-d326-7c03-8efd-198d9b0c267e" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol_01a18db9-d326-77dc-82a9-be2064775051" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_TradingSymbol"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_dei_EntityListingsLineItems_01a18db9-d326-7442-89b9-b1dfc745e0fb" xlink:to="loc_dei_TradingSymbol_01a18db9-d326-77dc-82a9-be2064775051" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName_01a18db9-d326-75cf-aa63-9e45754a04ce" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_SecurityExchangeName"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_dei_EntityListingsLineItems_01a18db9-d326-7442-89b9-b1dfc745e0fb" xlink:to="loc_dei_SecurityExchangeName_01a18db9-d326-75cf-aa63-9e45754a04ce" xlink:type="arc" order="2"/>
  </link:definitionLink>
</link:linkbase>
