The Frenchman had been at Lille since 2008, overseeing a Ligue 1 and French Cup double in the 2010-11 season.
The 49-year-old will take over from Aurelio Andreazzoli, who himself was a mid-season replacement for Zdenek Zeman.
“I’d first of all like to spare a thought for Lille, the president and the fans. They launched my professional career and allowed me to win my trophies as a coach. I am very proud and honoured to come to Roma,” said Garcia at a press conference in New York that was held in Italian, French and English.
“Roma need to return to Europe, but my role here now is to talk about objectives on the field. My philosophy of football is attacking, but I don’t forget that to win matches we need a solid defence.
“I am a faithful person and spent five years at Lille, so I hope to be at Roma for many years too.”
Roma president James Pallotta added: “We are very excited and confident that Rudi Garcia is the right coach for AS Roma. He is a proven winner with a great football mind who we believe fits in perfectly with our vision for the future."
“We have been following Garcia for a few years and he represents the union of the coaches we had and the coaches they could’ve been," sporting director Walter Sabatini said.
"They all brought something positive to the club and in my view Rudi represents the combination of all those best elements.
"Last but not least in our reasoning, his great desire for Roma. He has been thinking about the club for several days and wanted to prove to us his firm determination to come to Roma."