A product of Sporting's academy, the 27-year-old has been capped 49 times by his country and represented Portugal at the 2022 and 2026 World Cups. He joined Milan from French side Lille in 2019.
Leao became a key figure for the seven-time European champions, scoring 80 goals and providing 65 assists in 291 appearances across all competitions. He helped Milan win the Serie A title in 2021/22 and the Italian Super Cup in the 2024/25 season.
According to media reports, Milan have accepted a €45 million offer from Galatasaray for Leao, whose contract with the Italian club runs until June 2028.
"It's a difficult time," Leao told Sky Sport Italy on Friday after Milan's 2-0 Serie A win over Venezia at the San Siro, where he was not part of the squad.
"I've said goodbye to my teammates after seven years.
"Milan helped me grow and understand what top-flight football is all about. The time has come to say goodbye. I might have liked to say goodbye in a different way. The fans supported me even during the tough times.
"I know what I've achieved here; I'll go down in the club's history. All I can do is say thank you."
Milan appointed former Manchester United coach Ruben Amorim as manager in June after a disappointing campaign last season that saw them miss out on Champions League qualification.
They have since made a strong start to the new Serie A season, winning their opening two matches.
"My love for Milan will never end; even from afar, I'll always be watching them," Leao added.
"There are times when you have to make a decision and choose a different path.
"Today, Milan showed great quality and have a great manager. He's someone who can help Milan win major trophies. It's the sort of football I like...
"Life doesn't end here. I cried, I was moved."
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