The striker, who has scored three goals in 14 international appearances for the Netherlands, joined Burnley from Wolfsburg in a reported £12million (€14.4m) move in January, as the Clarets battled relegation from the top flight.
That fight ultimately ended in failure, with Weghorst scoring just twice in 20 appearances for the club.
While Manchester City legend Vincent Kompany is hoping to lead Burnley to an immediate Premier League return, he will have to do so without the services of Weghorst, who joins a side which finished a disappointing sixth in the Turkish Super Lig last term.
Burnley confirmed his departure via their social media accounts on Wednesday, wishing the 29-year-old luck at his new club.
Weghorst will be hoping his move to Istanbul allows him to rediscover his Wolfsburg form: In the 2020-21 season, he scored 20 Bundesliga goals, a tally only bettered by Erling Haaland (27), Andre Silva (28) and Robert Lewandowski (41).