The penalty was issued for failing to comply with the FCA Client Assets Sourcebook, which applies to safe custody assets and to client money.
It would have been £180 million had the firms not agreed a settlement early.
The failings found in the FCA probe "reflected a failure by the firms to consider properly the interests of their clients". These occurred between 1 November 2007 and 12 August 2013.
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Georgina Philippou, acting director of enforcement and market oversight at the FCA, said: "The size of the fine today reflects the value of safe custody assets held by the Firms as well as the seriousness of the failings and the fact that these failings were not identified by the Firms' own compliance monitoring.
"Other firms with responsibility for client assets should take this as a further warning that there is no excuse for failing to safeguard client assets and to ensure their own processes comply with our rules."
He said: "Our Custody Rules are in place to ensure that clients are protected in the event of insolvency.
"The firms' failure to comply with our rules including their failure to adequately record, reconcile and protect safe custody assets was particularly serious given the systemically important nature of the Firms and the fact that safeguarding assets is core to their business.
"Had the firms become insolvent, the total value of safe custody assets at risk would have been significant. This is compounded by the fact that the breaches took place at a time when there was considerable stress in the market."
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According to FCA officials, the failings meant that the firms were unable to meet their other obligations under the Custody Rules, such as the requirements to:
• conduct entity-specific external reconciliations;
• maintain an adequate CASS resolution pack (from 1 October 2012 when the requirement to do so came into force); and
• submit accurate Client Money and Asset Returns (CMAR) (from October 2011 when the requirement to do so came into force).
The FCA said the failings included:
• failing to take the necessary steps to prevent the commingling of safe custody assets with firm assets from 13 proprietary accounts;
• on occasion using safe custody assets held in omnibus accounts to settle other clients' transactions without the express prior consent of all clients whose assets were held in those accounts; and
• failing to implement CASS-specific governance arrangements that were sufficient given the nature of the firms' business and their failure to identify and remedy the failings identified.