The 30-year-old was on the transfer list as new manager Mauricio Pochettino did not have him in his plans.
Ziyech saw a January move to Paris Saint-Germain collapse after Chelsea failed to send in the papers to get the deal over the line.
A summer switch to the Saudi Pro League was also on the cards, but the transfer collapsed.
However, the Moroccan international is now set to leave Stamford Bridge three years after joining from Eredivisie giants Ajax.
Ziyech joined Chelsea in 2020 after establishing himself as one of the top playmakers in Europe. He notched 49 goals and 81 assists in 165 appearances for Ajax.
Several injuries made it difficult for him to get a head start in London, and he never kicked on from there. He has bagged just 14 goals and 13 assists in 103 appearances for Chelsea.
Ziyech will leave for Galatasaray, hoping to get more game time than he did at Chelsea.
The news comes after Chelsea triggered Michael Olise’s release clause. The Blues are trying to bring the French youth international to Stamford Bridge and will need to make space for him in the squad.
Ziyech will link up with other new Galatasaray signings such as Mauro Icardi, who joined permanently after spearheading them to the Super Lig title on loan last season.
Gala have also signed Kerem Demirbay, Tete, Wilfried Zaha, Angelino, Cedric Bakambu, Kaan Ayhan, Halil Dervisoglu, Gunay Guvenc and Caner Dogan.
Another big name could follow the attacker to Turkey, with Gala pushing to sign former Spain international Sergio Ramos.
Ramos has snubbed interest from Saudi Pro League and Major League Soccer clubs to continue in Europe.
Gala have offered him a two-year deal to earn €5.5 million annually. He is negotiating with the record-time Turkish champions.
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