Williams tweeted the signature on his one-year contract with Besiktas late Friday night from his verified Twitter account.
"Just made it official, headed to Turkey ...signed with Besiktas & @BJK_Basketbol," he wrote.
Williams' contract with Besiktas is worth $5 million, sources told ESPN.com's Chris Broussard.
Sources told ESPN.com's Marc Stein last week that Williams would not be required to report to the Turkish club before the end of August or early September and that his deal with them would include an immediate out that allows him to return to the NBA as soon as the work stoppage ends.
Williams has two years left on his contract with the Nets but is widely expected to opt out the final season, valued at nearly $18 million, to become a free agent in the summer of 2012.
Williams, 27, averaged 20.1 points and 10.3 assists for the Nets and the Utah Jazz last season.
Players under contract like Williams would typically need a letter of clearance from FIBA -- the sport's world governing body -- to play anywhere else. But the NBA Players Association has privately maintained for months that it intends to legally challenge any attempt by the NBA or FIBA to block a player such as Williams from playing elsewhere while the NBA has imposed a work stoppage.
"If they try to stop him," one source said of Williams, "the union will fight it."
The bigger risk for Williams is injury-related, especially after he was plagued by a wrist injury throughout the second half of last season after the Nets acquired him from Utah on Feb. 24. The injury required surgery on Williams' right wrist after the season.
Mike Mazzeo is a regular contributor to ESPNNewYork.com. Information from ESPN.com's Marc Stein was used in this report.