The defender has penned a four-year contract with the Turkish club after Fatih Terim's side beat arch-rivals Fenerbahce and Valencia to the Cameroonian
Talks began in April to bring the Cameroon international from the 2011 Ligue 1 champions to the Turkish club, though initially les Dogues were holding out for more than double the final fee.
Chedjou, 27, has signed a four-year contract with Fatim Terim's men and follows the likes of Wesley Sneijder and Didier Drogba in moving to the Istanbul giants in 2013.
He will be paid €2.2m per year as a basic wage, a €200,000 signing-on bonus and a €10,000 bonus for every appearance at the Turk Telecom Arena club.
Galatasaray were able to fend off interest from Spanish giants Valencia, Istanbul arch-rivals Fenerbahce and French contenders Monaco and Olympique de Marseille to secure the transfer.
The centre-back made 46 appearances for Lille this season and helped the club, with whom he has been since 2007, finish sixth in Ligue 1.