He was ordered off for a challenge on Leighton Baines midway through the second half.
The forward will be available for Saturday's Barclays Premier League match against Reading.
A statement from the FA said: "The FA can confirm that red cards shown to both Carlton Cole and Darron Gibson have been rescinded.
"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"Their three-match suspensions have been withdrawn immediately and written reasons will be provided at a later date."