Gay has been advising Birmingham City Council on a part time basis since announcing his retirement from Leeds earlier this year.
He will join the business as an associate in the CAS strategic advisory team.
David Whelan, managing director of the CAS treasury solutions business, said: “We are delighted to welcome Alan to our growing team.
“He brings a very strong understanding of the local authority sector which will further strengthen the range of expertise we can make available to our clients.”
Last year Gay was part of a team which conducted an independent review of Birmingham’s financial plans.
The review, which reported to the city council’s improvement panel, concluded that “a number of savings plans budgeted for in 2016/17 were very ambitious and in hindsight were unlikely to be achieved”.
Meanwhile, the planned sale of the CAS business by parent company Capita could happen as early as next month, according to reports.
The Times said that two private equity businesses are among the firms in the running.
CVC Capital Partners, which formerly owned Formula One racing, and GTCR, which owns the PR Newswire news outlet, are said to be among the frontrunners for the business.
A winner is expected to be selected at the end of May, The Times said. Investment bank Goldman Sachs is overseeing the process.
Capita is selling the business due to the need to cut its debt following financial difficulties caused partly by issues with Whitehall contracts.
None of the parties involved with the sale would comment on the process when contacted by Room151.