The Belgian centre-back was shown a straight red card by referee Mike Dean for a challenge on Jack Wilshere with 14 minutes remaining at the Emirates Stadium.
City were quick to announce their intention to appeal and, following a Football Association disciplinary hearing, have now confirmed their claim for wrongful dismissal has been upheld.
The FA has also released a statement which reads: "An independent regulatory commission has today upheld a claim of wrongful dismissal regarding Manchester City's Vincent Kompany.
"The defender was dismissed for serious foul play during his side's match against Arsenal on Sunday, January 13, 2013.
"As a result, Kompany's three-match suspension has been withdrawn with immediate effect."
Had the appeal failed, Kompany, 26, would have been banned for Premier League games against Fulham and QPR and an FA Cup fourth-round tie against Stoke or Crystal Palace.
The news will come as a big relief to manager Roberto Mancini, who is already short of central defensive options with Kolo Toure on Ivory Coast duty at the African Nations Cup and Micah Richards injured.
Joleon Lescott and Matija Nastasic are the club's only other fit and available senior centre-halves.
Dean's decision was widely criticised as Wilshere had taken a heavy touch and Kompany, in lunging towards the Arsenal man, made clear contact with the ball before his opponent.