The 33-year-old World Cup 2010 and Euro 2012 winner left Stamford Bridge at the end of the campaign after spending five seasons with the club.
During his time in London, he helped Chelsea win the Premier League, FA Cup and Europa League.
A statement on Roma website read: “I am delighted to be here at Roma.
“I’m excited for this challenge and to compete to achieve our targets over the coming seasons.
“I want to thank the fans for the welcome they’ve given me. I hope to make them happy.”