The left-back has signed a three-year contract with the Serie A club that will run until June 30, 2020.
"When I came in 2010, honestly, I didn't expect to play so long," Kolarov told City's official website. "Today is the day I have to say goodbye. Everything was quick the last couple of days. For me, it's a very sad day.
"In every part of the club we have improved not 100 per cent but 200 per cent. Now we are a far better club than what we were when I came. I am proud that I was part of making City the club that it is.
"For me it was a great pleasure to play for this shirt."
He added to Roma's website: "I am extremely happy to be here. I will give 100 per cent and more for Roma.
"My objective is always the same: to win."
Kolarov becomes Roma's seventh signing of an extremely busy transfer window for the club under new sporting director Monchi.
"Aleksandar is a player with vast experience who can immediately contribute to the team," Monchi, said. "I believe he will help us develop, on and off the pitch.
"I want to thank him for the enthusiasm and willingness he has shown in wanting to come to Roma."
Kolarov has already joined up with Roma's training camp in Boston. The Giallorossi face Tottenham in New Jersey on Tuesday.