Personal terms are not expected to pose a major stumbling block, with talks having taken place over the past few months, and Gundogan is now set to become the first signing of the Pep Guardiola era.
The Germany international's agent was pictured meeting City sporting director Txiki Begiristain in March as it became apparent that the Blues had stolen a march on Juventus and Barcelona, who had previously shown their interest.
City and Dortmund continued to haggle over the price in the interim, but have finally settled on a €26m (£20.1m) deal which will be topped up with performance related add-ons.
A dislocated knee cap has ruled Gundogan out of Germany's Euro 2016 campaign and will keep him on the sidelines throughout pre-season, but City have pushed ahead with the move.
The club have identified a list of priority targets to help smooth Guardiola's transition to English football, with Gundogan joined by Real Madrid's Toni Kroos and Juventus' Paul Pogba.
READ MORE | Inside Guardiola's City overhaul
Guardiola officially takes up office at the Etihad Stadium on July 1 but he is expected to step up his preparations after a short break.
The former Barcelona coach guided Bayern Munich to a league and cup double on Saturday, beating Dortmund on penalties in the DFB-Pokal final.
He admitted earlier this season that he had already started to keep one eye on his next job, and it is understood he will turn his full attention to City before the official start date on his contract.