Cole has travelled to the Italian capital, with Roma posting a photo on their official Twitter feed, with the message: "Welcome to Rome, Ashley!"
The 33-year-old is a free agent following his release by Chelsea in May and had been linked with a number of teams in both the Premier League and Europe.
Cole, long a lynchpin of the Chelsea and England teams, had become a fringe player in Jose Mourinho's squad last season.
The Portuguese coach preferred Cesar Azpilicueta at left back for much of the season in which Chelsea finished third behind champions Manchester City and Liverpool.
Cole made just 17 Premier League appearances, his lowest total in a single campaign for the club.
Since his move from Arsenal in 2006, he won one league title, four FA Cups, the Europa League and, the Champions League.
Cole earned 107 England caps, but announced his retirement from international football before the World Cup after he was left out of Roy Hodgson's squad for Brazil.