The 33-year-old free agent will earn 2.3 million euros ($3.14 million) (1.83 million pounds) a year, according to local media.
Roma, back in the Champions League after finishing runners-up to Juventus in Serie A last term, announced Cole's arrival in the Italian capital for a medical by publishing a photo of the left back on their Twitter feed with the message "Welcome to Rome, Ashley".
Cole was met at Fiumicino airport by a scrum of reporters and chanting fans.
He had eight trophy-laden years at Stamford Bridge, winning the Premier League, Champions League and Europa League, as well as four FA Cup titles.
Cole also earned 107 caps in 13 years as an England player but retired from international football after being left out of manager Roy Hodgson's 2014 World Cup squad.
Roma also announced the signing of Fenerbahce's Salih Ucan on Monday, with the 20-year-old Turkey midfielder agreeing a two-year loan deal that gives the club an option to buy him in 2016 for 11 million euros).
The Serie A team must pay Fenerbahce an initial fee of 4.75 million euros ($6.48 million) for the player.
According to media reports, Roma are also keen to sign former Barcelona and Chelsea striker Samuel Eto'o.
The Cameroon forward won the Champions League with Inter Milan in 2010 and Roma are said to be preparing a one-year deal for the 33-year-old free agent.
(Editing by Tony Goodson)
