Portuguese striker Rafael Leao, whose declining form coincided with AC Milan's slide in recent seasons, joined Galatasaray on Sunday, the Istanbul-based club announced.
The four-time reigning Turkish champions, who have qualified for the Champions League, said they had paid €38 million ($44mn) for the 27-year-old attacker, who was also being courted by Aston Villa.
Galatasaray said he signed a four-year contract worth €10 million a year.
The Portuguese international had been welcomed by a crowd of supporters when he arrived in Istanbul on Saturday.
"Twenty per cent of the profit made on the player's next transfer will be paid to AC Milan," the Turkish club added in its statement.
The Sporting Lisbon academy graduate will play alongside Nigerian Victor Osimhen, the Turks' star striker, and former Bayern Munich winger Leroy Sane.
After arriving for a club-record €49.5 million from Lille in 2019, Leao scored 80 goals in 291 games for Milan. He was a key figure in their 2021-22 Serie A triumph, but concerns over his commitment and declining production clouded the end of his time at the club.
Earlier this summer, Milan broke their club record when they paid €74 million to acquire another Portuguese attacker, Goncalo Ramos, from Paris Saint-Germain.
"It's a tough moment saying goodbye to my teammates after seven years," Leao said on Friday after watching Milan beat visiting Venezia 2-0.