City did not disclose financial details of the deal but British media reported that Guendogan would cost the Premier League club around 20 million pounds.
"I'm thrilled to have signed for Manchester City," Guendogan said in a statement on City's website (www.mcfc.co.uk).
"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."
The injury-prone German international dislocated a kneecap in training in May, ruling him out of the 2016 European Championships in France.
Guendogan, who also missed the 2014 World Cup with a back injury, made more than 150 appearances in five years at Dortmund after being recruited by Juergen Klopp, who is now in charge of Liverpool.
The midfielder was part of Klopp's Dortmund side that won a domestic double in Germany in the 2011-12 season and reached the Champions League final in 2013, where they lost to Bundesliga rivals Bayern Munich.
"We celebrated many victories and stood together in moments of defeats," Guendogan said in a farewell note to Dortmund posted on his official Twitter page.
"I am very thankful to all my team mates and to the fans who always supported me."
(Reporting by Nivedita Shankar in Bengaluru; Editing by John O'Brien)
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