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.
Johnson, whose contract at the Riverside was due to run out at the end of the season, scored 13 goals in 96 games for Boro after making his debut in 2005, and also enjoyed a successful loan spell at Watford in 2007.
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.
Watch Johnson's goals for Boro against Doncaster last week
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