The Germany international, who is ruled out of Euro 2016 due to a knee injury, becomes new City boss Pep Guardiola’s first signing since taking over from Manuel Pellegrini.
The 25-year-old confirmed the news in a video posted on City’s official Twitter feed.
He said: “Hello City fans. You have been tweeting me for a long time and now I officially announce that I am a Manchester City player. Hope to see you soon.”
Gundogan, who made 157 appearances for Bundesliga giants Dortmund over a five-year spell, added on mcfc.co.uk: “I’m thrilled to have signed for Manchester City.
“When I learned of City’s interest my heart was set on coming here and things have moved very quickly.
“I have loved my time with Borussia Dortmund and I would like to thank the club and the supporters for the five very happy years I spent there.
“They gave me a platform to play on and I became a better player because of the belief, patience and trust they showed in me.
“Now I have a new challenge and that is to achieve great things with City. The opportunity to work with a coach like Pep Guardiola is something I am really looking forward to and I am flattered to be the first signing the club has made this summer.
@MCFC ANNOUNCE GUNDOGAN! 😉
— Ilkay Gündogan (@Guendogan8) June 2, 2016
“I can promise the City fans I will give everything to help us win titles both in England and the Champions League. These are exciting times.
“I have my best years ahead of me and I think we can achieve great things together. I can’t wait to begin this new chapter in my career.”
Manchester City’s director of football Txiki Begiristain added: “Ilkay is an excellent addition to our team and we are delighted to have him on board.
“He is an intelligent and versatile midfielder who can operate in a number of different roles. I think our supporters will enjoy his work ethic and technical ability and I believe he will be a very important player for us in the coming years.”
Gundogan has won 16 caps for Germany, scoring four goals.
