Johnson travelled to Manchester for talks on Monday afternoon after the two clubs agreed an undisclosed fee.
The 22-year-old passed a medical and signed a contract until June 2014.
City boss Roberto Mancini said: "Adam is a very good player with fantastic potential, and as a club we are always keen to sign British talent."
Johnson will wear the number 11 shirt for City, and goes straight into Mancini's squad for Saturday's trip to Hull.
Boro fan here. As sad as it is to witness us losing our best player, I have no doubt he'll force his way into the England World Cup squad
Daring Back Marker
The former England Under-21 international has been in impressive form in the Championship this season and also briefly shone against City in the FA Cup before coming off injured midway through their third-round clash at the start of January.
Mancini's other attempted deadline-day signing, that of Parma midfielder McDonald Mariga, fell through earlier on Monday after the Kenyan international failed to secure a work permit.
There were also reports from Spain that City were trying to complete a last-minute deal for Real Madrid midfielder Gago, but BBC Sport understands that any talks over a possible loan move for the Argentina international had long-since stalled.
Source: BBC Sport
Source: BBC Sport