The Bosnia-Herzegovina international moves to the Stadio Olimpico on a season-long loan deal, with Roma retaining an option to make the move permanent.
City announced the deal with a lengthy tribute to the former Wolfsburg striker, who lifted two Premier League titles in his time in Manchester.
"A firm favourite with the City fans and backed by an adoring nation of Bosnians, 'The Diamond' shone brightly during his time with the Blues and will be fondly remembered for having a pivotal role in City’s glorious past five years," read a release via their official website.
"Everybody at the Club wishes Edin the very best for the future and thank him for his excellent service with Manchester City."
Speaking after completing a medical and signing a contract in Italy, Dzeko told Roma TV: "I came here to win titles with Roma. Hopefully we will win many, many trophies but first we have to work hard on the pitch and at the end, hopefully we will get where we want to be.
"I can only promise one thing and that is that I will give my best for this club in every game."
Dzeko's arrival comes after Roma allowed Antonio Sanabria to return to La Liga on a season-long loan deal with Sporting Gijon.
The 19-year-old had struggled for game time under Rudi Garcia and could turn out for his new side in their pre-season clash with Villarreal on Saturday.
