The Bosnia international scored 72 goals in 189 appearances for City since joining from Wolfsburg in January 2011, but saw his influence wane in an interrupted 2014/15 campaign in which he scored only six times.
According to statements released by both clubs, Dzeko's move to the Eternal City will become permanent if the 29-year-old meets certain targets in the coming season
Dzeko said on the Roma website: "I came here to win titles with Roma
I hope we will win many trophies but first we have to work hard on the field and in the end, we can get where we want
I can only promise you one thing: I will give my best to this team in every game."
The Italian club issued a statement saying they had paid four million euros (£2.86million) as a loan fee, while securing an agreement that the deal will become permanent for a further payment of 11million euros (£7.875million) on "condition of the occurrence of certain sporting situations".
While not always a regular starter, Dzeko made a huge contribution in his first full season with City.
He scored 19 goals in 42 appearances including the stoppage-time header which made it 2-2 against QPR before Sergio Aguero's winner in the fourth minute of time added on secured the Premier League title.
He signed a new four-year deal last summer but as he failed to spark last season he began to be linked with a move away, and Roma have been pursuing his signature for several weeks.
He leaves Manchester a two-time Premier League winner, having also lifted the FA Cup and League Cup
He scored 50 Premier League goals in 130 appearances.
City have also allowed Stevan Jovetic to leave this summer, with Academy graduate Kelechi Iheanacho expected to offer back-up to senior strikers Aguero and Wilfried Bony, while new signing Raheem Sterling can also operate as a centre-forward.
The Manchester club continue to be linked with a move for former Chelsea playmaker Kevin De Bruyne.
Source : PA
Source: PA