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"As a result, Kompany's three-match suspension has been withdrawn with immediate effect."