Tuncay has completed his move from Stoke to Wolfsburg.
The Turkey striker has signed a three-and-a-half-year contract at the VW Arena, the Bundesliga club have confirmed.
The 29-year had a medical with Steve McLaren's men on Monday.
The fee has not been revealed but is believed to be around £4m.
Tuncay made 55 appearances, including 26 starts, during his 18 month stay at the Britannia Stadium and scored 8 goals.