Gibson was dismissed by referee Anthony Taylor for a high challenge on Mark Noble in Everton's 2-1 win at Upton Park, a game that also saw West Ham striker Carlton Cole sent off for a challenge on Leighton Baines.
Everton lodged their appeal with the Football Association on Christmas Eve, meaning Gibson was able to face Wigan yesterday, and announced on their website today that the dismissal had been quashed at a hearing.
It means the former Manchester United player will not face a three-match ban.
Cole has also seen West Ham's appeal over his red card upheld by the FA.
He was ordered off for a challenge on Leighton Baines midway through the second half.
"Both players were sent from the field of play in the Premier League fixture between West Ham United and Everton at Upton Park on Saturday 22 December.
"Their three-match suspensions have been withdrawn immediately and written reasons will be provided at a later date."