Gundogan left Manchester on the back of the club’s greatest season, lifting the Premier League, FA Cup and Champions League trophies within the space of a month, according to skysports.com.
He spent seven years at the Etihad Stadium since joining from Borussia Dortmund in 2016, and manager Pep Guardiola had publicly hinted at his own desire to extend that stay further.
Gundogan was in talks with City over a new deal ahead of his contract expiry at the end of last week.
However, the length of the deal on offer for the 32-year-old - one year plus an option of a further 12 months - was a sticking point, and he has instead penned a two-year contract, also including a 12-month option, with LaLiga champions Barcelona. His release clause has been set at €400m (£342m).
Gundogan told the Manchester City club website: “For me, it has been a total privilege and pleasure to be part of Manchester City for the last seven years.
“Manchester has been my home and I have felt part of a very special family at City.
“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.
“First, I would like to thank Pep. 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.
“I will carry City always in my heart. Once a blue, always a blue.”
Writing on the Player’s Tribune website, Gundogan said announcing to his teammates he was leaving City was his hardest goodbye in football, and explained why he had chosen Barcelona as his next, and perhaps final, move in his career.
He wrote: “Goodbyes are never easy, but it’s even harder with this team. When I had to break the news to the boys that I was leaving in our group chat, I was very emotional. I will miss all of them, honestly.
“But I am happy to say that I’m leaving here as a champion, and I have nothing but love for the club in my heart. This season, something clicked. I just knew we were going to do it.
“I don’t even mean just the Champions League. The Premier League, the FA Cup - everything. Week after week, I just felt everything lining up perfectly. Even when we were 10 points behind Arsenal, I knew we would win the league.”
Addressing his decision to join Barca, he added: “If I was going to move, there is only one club in the world that made sense. It was Barcelona or nothing.
“Ever since I was a little kid, I dreamed of wearing that shirt some day. I am confident that I have a few more years left at the highest level, and I just want to help bring Barcelona back to where they deserve to be.”