The winger has signed a four-year deal with the Black Eagles after failing to make the grade in the Premier League.
Nkoudou moved from Marseille to Tottenham in 2016 but saw his first-team opportunities severely restricted.
Now he will look to relaunch his career in Turkey after leaving north London on Thursday.
"We have reached agreement with Turkish Super Lig side Beşiktaş for the transfer of Georges-Kevin Nkoudou," Spurs confirmed on their official website.
We wish 'GK' all the best for the future.
The 24-year-old has had loan spells with Burnley and Monaco and has now been allowed to leave Spurs for a reported €5 million (£4.52m/$5.5m) - less than half the fee that Tottenham originally paid Marseille for his services.
Nkoudou's sale is the latest piece of business in what has been a hectic transfer period for the Champions League finalists, following several windows of almost non-existent activity.
Tanguy Ndombele, Ryan Sessegnon, Giovani Lo Celso and Jack Clarke were all signed by Spurs over the summer, although the latter returned immediately to Leeds United on loan.
Mauricio Pochettino's men have started the 2019-20 season with victory over Aston Villa followed by a thrilling 2-2 draw with Manchester City, with Newcastle United's visit to London on Sunday their next Premier League engagement.