The 31-year-old attacker spent last season on loan with Gala and the confirmation of his move brings an end to a four-year association with the West Londoners.
Ziyech joined the Blues from Ajax in 2020 for a fee of £34m but struggled to establish himself as a first-team regular at Stamford Bridge.
However, the Morocco international did win the Champions League with Chelsea in his first season in England, scoring two goals in 10 matches, though he was an unused substitute in the final against Manchester City.
He was loaned to Galatasaray after the Blues' former boss Mauricio Pochettino indicated he was not part of his future plans.
Chelsea confirm Hakim Ziyech free transfer to Galatasaray
Ziyech had a successful 2023-24 campaign in Turkey, tallying six goals and three assists in 18 Super Lig appearances as Gala held off Fenerbahce to earn their 21st top-flight title.
The Moroccan has now completed a permanent move to Rams Park, penning a one-year deal with the Turkish champions, with an option to extend that by another 12 months.
"Hakim Ziyech has completed a permanent transfer to Galatasaray. We thank Hakim for his efforts during his time at Chelsea and wish him well as he begins the next chapter of his career," Chelsea announced on their official website.
Ziyech was previously linked with a loan move to Paris Saint-Germain in January 2023 but the deal collapsed on deadline day despite his trip to the French Capital.
A statement from Galatasaray following the confirmation of the deal added: "Professional football player Hakim Ziyech's final transfer was made free of charge as the free purchase option conditions in the temporary transfer contract were met.
"The football player will be paid a net seasonal wage of 2,850,000 euros for the 2024-2025 season. In addition, in accordance with the agreement, if the conditional extension option is realised, the football player will be paid a net seasonal salary of 2,850,000 euros for the 2025-2026 season."
Is Ziyech the first of many Chelsea departures this summer?
Ziyech made a total of 107 appearances for Chelsea and scored 14 goals while providing 13 assists during his time at Stamford Bridge.
However, the Moroccan international is not the only player who is expected to depart West London this summer.
Chelsea also confirmed the sale of Ian Maatsen to Premier League rivals Aston Villa for a reported fee of £38m this week.
Additionally, the Blues are believed to be under pressure to make a few more player sales to avoid breaching Profit and Sustainability Rules.
Recent reports have suggested that the club are open to offers for academy graduates Trevor Chalobah, Conor Gallagher and Armando Broja in the current transfer window.