The 26-year-old Albania international has completed a move to the Turkish club following the Black Cats' decision to accept a bid of in excess of 6million euros for his services.
Despite establishing himself as a crowd favourite at the Stadium of Light, Cana has moved on after just one season.
He said: "Since the first day I arrived, I have had an amazing story with Sunderland.
"I knew I would find the kind of club and support I needed to play my game.
"The people here love their club, they have passion and a proper identity. I gave my all for the club and it will always be in my memory.
"I have been offered the opportunity to play in European competition and the Champions League, and especially to be closer to my family.
"This was not an easy decision for me though and I hope people understand.
"I thank everyone at Sunderland - the coaching staff, medical team, office staff, my team-mates and of course the fans.
"I wish the club to achieve everything it deserves and to continue moving higher and higher."
Cana joined the Wearsiders in a £5million switch from Marseille last summer and was an instant hit as his robust style of play endeared him to the club's fans.
He made 35 appearances last season, two of them as a substitute, although he was sent off once and picked up 10 bookings along the way, which was a concern for Sunderland manager Steve Bruce.
Bruce said: "Lorik's style of play and attitude made him a natural choice as captain last season, but when he came back for pre-season training, it was apparent that he had a desire to return to Europe.
"Turkey is nearer to Albania, where his family and roots are, and it is much easier for him to see them on a more regular basis - I think this was a major factor for him.
"We thank Lorik for his time here and wish him the best of luck for the future."
Despite Cana's departure, Bruce will still have Lee Cattermole as a holding midfield player, while youngster Jordan Henderson shone last season and fellow Academy graduate Jack Colback has been challenged to make a similar step up after his successful spell on loan at Ipswich.
In addition, the Black Cats have already added Paraguay midfielder Cristian Riveros to their squad, although the South American is currently enjoying a break after his exertions at the World Cup finals.
The versatile Riveros lined up in the playmaker role for his country in South Africa, but can also operate in a wide position.
Sunderland returned for pre-season training on Wednesday as Bruce continued his search for new recruits.
Indeed, they were joined at the Academy of Light training headquarters this morning by Argentinian full-back Marcos Angeleri.
However, no deal for the Estudiantes defender, who has three senior international caps, has been agreed yet.
Meanwhile, the Black Cats have been linked with a move for Ghana international striker Asamoah Gyan following his fine World Cup.
But it is understood Sunderland contacted Rennes before the tournament got underway and are yet to return with a firm proposal.