The former Arsenal captain returns to England after two years away, where he helped Bayer win the Bundesliga in his first season.
Xhaka, 32, joins for an undisclosed fee and has signed a three-year contract at the Stadium of Light.
He said: "I’m very proud to be here. When I spoke to the club, I was excited and I felt the energy, and the mentality all the people and players have.
"It’s exactly what I wanted, and I have a very good feeling. We are back to where this club needs to be, and we want to stay here to write our own history.
"I feel I’m ready to help the team with my experience but with quality as well. We need to find ourselves on the pitch, but I don’t think this will be a big problem. It’s been a long time to wait, but I’m here now and I’m looking forward to it.”
Massive statement
Sunderland manager Regis Le Bris also stated: “First of all, it’s a massive statement about the attractiveness of the club. If a player of that dimension says yes to our project, it means something.
“I have to congratulate the people behind the scenes for completing the move. It makes a big noise and that is something we are looking to do this season.
“For the squad, it’s really important. We started our recruitment with talented young players but the second layer is to balance the squad with more experience. With what he has achieved in the game, Granit is really good for that. It’s really clear what he will bring to the squad. At the same time, his level his high.
“He brings many things for the balance of the squad. He’s a captain, a leader, has strong experience in the Premier League and the national team. This piece in our structure will be really important to balance the squad. We’re really happy.
“He’s still at top with a specific style of play so it’s really important to feel these pillars in our structure because it gives confidence to everyone for the Premier League.”