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"As a result, Kompany's three-match suspension has been withdrawn with immediate effect."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.
Kompany took to Twitter after the game to state his case.
He wrote: "No grudges against the referee, I understand the difficulty of the job.
"About the tackle: If the ball is overrun by the opponent and a 50/50 challenge occurs, collision is inevitable.
"Ultimately I'm a defender: Appeal may work or not. I will never pull out of a challenge, as much as I will never intend to injury a player."
City were already 2-0 up when the incident occurred and held onto their lead without further alarm.
The success of Kompany's appeal comes after the FA similarly rescinded red cards for West Ham's Carlton Cole, Darron Gibson of Everton and Stoke's Steven Nzonzi last month.
Kompany's availability may ease speculation that Mancini may be forced into the transfer market to find defensive cover this month.
It had been understood that Mancini would not be able to recruit unless other players left and the Italian has repeatedly said he does not want to sell anybody.
Meanwhile, striker Carlos Tevez is considering whether to stay with the club beyond his current contract.
The 28-year-old's present deal is due to expire at the end of next season.
The Argentinian, quoted in The Sun, said: "I've one year left on my deal and City want me to sign for two more seasons. I'll think about it.
"This year is different from last, when I wanted to end the contract with City. I'm happy here as they are treating me well.
"Sometimes I play, sometimes I don't, but that's okay."