It means Tadic will be moving back to the Dutch league, having joined Southampton from Twente four years ago.
He has been one of the brighter sparks in what was a poor Southampton team last season, and many fans will not be pleased to see him leave.
He scored 23 goals in his 162 appearances, helping the 'Saints' to three top-eight finishes in the league.
In a statement, Southampton said: "Everyone at Southampton Football Club would like to thank Dušan for all of his efforts during his four years at St Mary’s, and we wish him every success in the future."
The Serbian is currently in Russia on international duty, and his side will face Brazil on Wednesday night as they attempt to qualify from their group.
27 June 2018