Gibson was dismissed by referee Anthony Taylor for a challenge on Mark Noble in Everton's 2-1 win at Upton Park in a game that also saw Hammers striker Carlton Cole sent off for a challenge on Leighton Baines.
The paperwork needed to be submitted to the Football Association by 1pm on Monday but the appeal means Gibson will be able to play in the Boxing Day match against Wigan Athletic, with the case due to be heard on December 27.
Source: PA
Source: PA