His contract with La Viola is valid for a year, with a further season optional, depending on the fulfillment of the conditions.
Dzeko spent the last two seasons with Fenerbahce and leaves the Turkish club, coached by Jose Mourinho, on a free transfer.
Now 39 years old, he returns to Italy, where he played for Roma and Inter Milan.
Dzeko scored 21 goals in 53 games in all competitions for Fenerbahce last season, which shows that he still has what is needed.
In his career, the Bosnian striker played for Zeljeznicar in his home country, Usti Nad Labem and Teplice in the Czech Republic and the German club Wolfsburg, where he made a name for himself.
He came to Man City for £ 27 million in 2011, before he continued to Roma, Inter and then Fenerbahce.
Dzeko clocked 141 international caps for Bosnia, scored 68 goals and picked up 29 assists.