It emerged earlier this week that City had agreed a fee with Leeds to sign the midfielder, but it has gone a little quiet since.
Talks have been going on behind the scenes over personal terms, and those talks have now been concluded.
According to Fabrizio Romano, everything has been signed, and the deal has been completed, with only the official announcement remaining.
The medical has also been completed, with an agreement also in place for City star Dark Gyabi to join Leeds on a deal worth around £5million.
According to the report, Phillips turned down two other proposals to join City this summer.
The deal is set to be worth between £45million and £50million, with Phillips joining a rather crowded City midfield.
As far as defensive midfielders go, Rodri is the starter in that position, and he is coming off the back of a superb season, earning himself a new contract.
Phillips faces a tough task to replace the Spaniard.