Arsenal were also keen to sign Gundogan, but the midfielder has opted for a new challenge in Spain after seven years at the Etihad Stadium.
Gundogan leaves the Premier League champions with 14 trophies – five Premier League titles, one Champions League, two FA Cups, four Carabao Cups and two Community Shields.
“I have been lucky to have experienced so many unforgettable moments in my time here and to have been captain for this extra special season has been the greatest experience of my career,” he said.
“First, I would like to thank Pep [Guardiola, Man City manager]. To have been able to play under and learn from him for so long has been something I will never forget.
“I would also like to thank all my team-mates – past and present – who have all played such a special part in making my time here so amazing.
“Finally, I would like to thank the incredible City fans. They have supported me from the moment I arrived, and I owe them all so much for their support.
“This club made me realise all my dreams and I will forever be thankful for this opportunity.”
More follows.
