The former England left-back decided to seek a new challenge after running down his contract at Chelsea, and is set to sign a two-year deal worth £38,000 per week after tax
Ashley Cole has arrived in Italy on Monday to finalise a free transfer to Roma.
Goal understands the former England defender has been offered a two-year contract by the Serie A club which is worth £1.98 million per year net of tax, equivalent to £38,000 per week after taxes.
Roma have confirmed Cole's arrival in the city via their official Twitter page, with the player now understood to be set for a medical after agreeing to the deal in principle.
The 33-year-old is a free agent after leaving Chelsea in June following eight trophy-laden seasons at Stamford Bridge.
Cole 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.
Despite interest from the likes of Liverpool, Tottenham and AC Milan, Cole has settled on Roma, who 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 finalised.
Cole is a three-time Premier League champion, twice with Arsenal and once with Chelsea, and also has seven FA Cup winners' medals - more than any other player - 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.