His contract with La Viola is valid for one year, with a further season optional, subject to the fulfilment of terms.
Dzeko spent the last two seasons with Fenerbahce and leaves the Turkish club, coached by Jose Mourinho, on a free transfer.
Now aged 39, he is returning to Italy, where he played for Roma and Inter Milan.
Dzeko scored 21 goals in 53 games in all competitions for Fenerbahce last season, proving he's still got what it takes.
In his career, the Bosnian striker has played for Zeljeznicar in his homeland, Usti nad Labem and Teplice in Czechia, and German club Wolfsburg, where he made a name for himself.
He joined Man City in 2011 for £27 million, before moving on to Roma, Inter and then Fenerbahce.
Dzeko has clocked up 141 international caps for Bosnia, scoring 68 goals and notching up 29 assists.