ESPN's Marc Stein confirmed the report, saying that Williams won't be required to join the team before the end of August.
Williams, who is under contract with the New Jersey Nets for the 2011-12 season, will most likely need a letter of clearance from FIBA to play elsewhere.
According to Yahoo! Sports, Williams will make $200,000 per month.
The Turkish television station also reported that Hawks center Zaza Pachulia is also planning on joining the Turkish club.
Besiktas is widely known for signing former NBA star Allen Iverson to a two-year deal in 2010.
Williams, 27, was traded from the Utah Jazz to the Nets in a multi-player deal in February.