The Turkey captain joins former Boro team-mate Robert Huth at the Britannia Stadium after the Germany defender sealed his switch from Teesside a day earlier.
Tony Pulis: "Tuncay is an exciting player with his pace and skill who will certainly get the crowd going.
"He is also a player of international calibre and a leader of his national team.
"Robert has a great presence about him.
"He is a big, strong defender and the fact he has played nearly 20 times for Germany is some recommendation in my book.
"He's one you know you can lean on."
Chief executive Tony Scholes: "We are delighted to bring a player of Tuncay's quality to the club because he has attracted attention from a number of big clubs, as indeed had Huth.
"Therefore this is a powerful statement of our intentions as we look to move the club forward."