Sources say the former England left back has decided to seek a new challenge after his Chelsea deal expired and will sign a two-year deal worth 38,000 pounds per week after tax.
The former England defender has been offered a two-year contract by the Serie A club which is worth 2.5 million euro per year net of tax, equivalent to 48,000 euro per week after taxes.
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Sources have told Goal UK that the deal is agreed to in principle and there are only the formalities to be completed, including a medical.
The 33-year-old is a free agent after leaving Chelsea in June following eight trophy-laden seasons at Stamford Bridge.
He was offered a new contract by the Blues on reduced terms and decided to find a new challenge following the end of his international career, which came when he was excluded from England's World Cup squad in May.
Despite interest from a host of clubs at home and abroad, including Liverpool, Tottenham and AC Milan, Cole has settled on Roma, which will compete in next season's Champions League after finishing second in Serie A last season.
His agent, Jonathan Barnett, has admitted Cole has been considering a move abroad although he denied that a destination had been finalized.
Cole is a three-time Premier League champion, twice with Arsenal and once with Chelsea and also has seven FA Cup winners' medals and won the 2008 League Cup.
He was also part of Chelsea's Champions League winning team in 2012 and went on to win the Europa League a year later.