Osman, 22, was a second-round draft pick in 2015, and the Cavs kept him in Europe for two seasons.
His signing and joining the Cavs for next season was widely expected -- Osman spent last weekend with team officials in Las Vegas for the start of NBA Summer League.
Cleveland is also paying $700,000 toward Osman's $1 million buyout of his contract with Anadolu Efes, his Turkish club.
The Cavs are using a portion of their $5.2 million exception to the salary cap to pay Osman. It was their intention to do so, which is why they decided not to offer a contract to free agent Jamal Crawford -- who was looking for the full exception from Cleveland.
According to ESPN, the Cavs have $2.4 million of their exception left. They are projected to pay nearly $71 million luxury tax penalties alone.
The Cavs now have 14 players under contract, leaving one roster spot plus two two-way contracts for G League players. They've brought back Kyle Korver and added Jose Calderon and Jeff Green since free agency started July 1.
Osman, who is 6-8, averaged 7.1 points and 2.8 rebounds in Euroleague play last season, shooting .340 from 3-point range. He's a high-energy player with the ability to defend the wing. A team source said he could become a player in the mold of Trevor Ariza.
Osman did not participate in Cleveland's Summer League games because of a commitment with the Turkish national team. He left Las Vegas on Sunday to return home.
Through a Cavs spokesman, Osman declined an interview request from cleveland.com in Las Vegas.
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