The former England defender has been handed a contract by the Serie A club that is worth 2.5 million euros per year.
He was offered a new contract by the Blues on reduced terms but decided to seek 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 opted for Roma, which will compete in next season's Champions League after finishing second in Serie A last season.
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.