Dzeko has signed a two-year contract with his new club.
The 37-year-old ends a two-year stay with the Nerazzurri, where he won two Coppa Italia trophies and helped them reach last season's UEFA Champions League final, losing to another of his former sides, Manchester City.
Dzeko's exit brings to an end an eight-year stay in Italy, where he scored 147 goals and produced 69 assists for AS Roma and Inter Milan.
The Bosnia and Herzegovina international will go in as a replacement for Enner Valencia, who has joined Internacional in Brazil.
"To inform. World-famous striker Edin Dzeko will come to Istanbul to pass the health checks and complete the transfer negotiations. We present it to the public," announced Fenerbahce on social media.
"Goodbye Inter, it's been two wonderful years," Dzeko wrote on Instagram. "It has been an amazing journey. We're parting ways now, but thank you."
Fenerbahce finished second in the Turkish Super Lig last season.
