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 Wolves, who are struggling in 12th place in the Bundesliga, had been on the look-out for striking reinforcements after selling Edin Dzeko to Manchester City.
They have also brought in Germany frontman Patrick Helmes from Bayer Leverkusen.