The Brazil international, whom Juventus signed for £21 million, will remain in Istanbul after spending the last two seasons on loan with the Turkish champions
The Super Lig champions also confirmed that the Brazil international, who has spent the last two seasons on loan at the Turk Telekom Arena, has agreed a contract with the club that will net him €3.1m [£2.6m] per year.
Juventus, who acquired Melo from Fiorentina for a reported combined total of €25m [£21m] in 2009, had been the first of the parties involved to confirm the player's departure on their official website on Saturday morning.
"Felipe Melo will continue to wear the Galatasaray shirt," a statement read. "Having played in Istanbul for the last two seasons, the Brazilian will now, in effect, completely belong to the Turkish club."
Melo, 30, who has been capped 22 times by Brazil, has won back-to-back league titles in his two seasons in Turkey to date.