STOKE manager Tony Pulis said he had helped Tuncay realise "a dream" by allowing the striker to move to Wolfsburg for £4.5million after 17 months at the Britannia Stadium.
The 29-year-old Turkey captain agreed personal terms with the Bundesliga side and passed a medical on transfer deadline day.
Pulis said: "Tunny came to me at the weekend and asked me if the club would help him to achieve his dream.
"He has always wanted to play in Germany and missed out on several occasions in the past.
"So this is a fantastic opportunity for him, and it is a fantastic deal for the club when you consider what we paid for him when he signed from Middlesbrough.
"I spoke to Tunny a number of times about his hopes and ambitions in his playing career and it was quite apparent that he saw Germany as a great opportunity not only to be much closer to home but also to boost his international prospects as well."
Tuncay recently posted his top 10 goals on Facebook, leading to speculation he was trying to engineer a move. He later denied that was the reason behind the video.
However Pulis praised the player for his contribution to the club.
He said: "Despite all the speculation, Tunny has been a smashing lad to have around the place; indeed a credit to both himself and his profession.
"He wanted to move last summer, but the time wasn't right then. Now though, we have brought in John Carew, and Mamady Sidibe is back from injury, so we have plenty of options.
"You want that competition for places, but you can't keep everyone happy. This move suits Tunny's needs and everyone here wishes him well in the future."
Tuncay felt it was too good an opportunity to turn down.
He said: "On three occasions, moves to Germany have fallen through at the last minute, so I am delighted, but also relieved, that this time I have been able to make the most of this opportunity.
"I would like to thank the manager and everyone at the club and, of course, the supporters for making me feel so welcome. I can assure you I would not have joined another English club, but this was too good an opportunity for me to fulfil my dream."
Tuncay joined Stoke in August 2009 when he completed a £5 million transfer from Middlesbrough, the club where his new manager at Wolfsburg, Steve McClaren, had a successful spell in charge.