The 19-year-old winger, who has been capped four times by Turkey, has signed a five-year contract with the Super Lig club.
Fulham manager Martin Jol has backed Frei to make a significant contribution at his new side and says that the lack of first-team opportunities was the primary reason for the midfielder's sale.
"Kerim has progressed well through his time in the academy and into the fringes of the first team, which enabled him to play for the Turkish national team, which is a big thing for him," the Dutchman told the club's official website.
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"He's sure to have a big impact back in Turkey and I know that, on a personal level, it's a good option for him. As a club, because of the structure of the deal, we are still invested in his future and what we believe he'll be able to achieve in time. I know he'll be much happier playing, so we wish him all the best."
Frei says that he has developed during his time at Craven Cottage and is relishing the prospect of playing in Turkey.
"I've really enjoyed my time at Fulham and I'm grateful for all of the support I received both as a young player in the academy and with the first team," the youngster enthused. "It's a great club, with good people and great fans, and it helped me a lot with my progression.
"Now it's time for my next step and I'm very excited about playing for Besiktas, and in Turkey, where I know that I'll be really happy."