Tony Pulis signed Huth on Thursday and now Tuncay has followed in the German defender's footsteps by leaving The Riverside in search of top flight football for a fee of £5m.
Tuncay, 27, was Middlesbrough's top scorer last season as they suffered relegation, scoring seven goals in 33 Premier League appearances for Gareth Southgate's side.
As captain of his national side, the forward is a player of some stature as well as skill and Pulis was understandably delighted to make the Turkey star his second signing in 24 hours.
"Tuncay is an exciting player with his pace and skill who will certainly get the crowd going," Pulis told the club's official website. "He is also a player of international calibre and a leader of his national team."
Stoke are also reported to have agreed a fee with Sunderland for defender Danny Collins.