BBC meanwhile report that the City paid approximately £20 million for the Germany intentional of Turkish origin.
Gunodgan also sent out a tweet confirming the move and another explaining why he decided to make the move.
Gundogan was expected to join Germany for the European Championships this summer but will miss the tournament due to injury.
The 24-year-old marks who also missed the 2014 World Cup with injury has become the first transfer of the Pep Guardiola era.
Gundogan will also be reunited with former manager Jurgen Klopp in the Premier League next season although he will be playing for an opposing side this time around.
The midfielder initially joined Dortmund from Nuremberg in 2011 under the stewardship of Klopp and helped the Bundesliga giants reach the 2013 Champions League final.
Gundogan signed a contract extension last season that still had a year to run.