The two players have had their three-match bans overturned after appealing to the Football Association's regulatory commission on Thursday.
Both players were given their marching orders for raising their foot to challenge for the ball during the game on Dec. 22 - plays that were deemed dangerous by referee Anthony Taylor; however, their three-match bans have now been overturned by the FA regulatory commission, who stated the players had been wrongfully dismissed after both sides lodged appeals.
“The FA can confirm that red cards shown to West Ham United's Carlton Cole and Everton's Darron Gibson have been rescinded," a statement from the FA read. “Both players were sent from the field of play in the Premier League fixture between the two clubs at Upton Park on Saturday 22 December. Their three match suspensions have been withdrawn immediately."
Hammers boss Sam Allardyce has expressed delight at the news that Cole will be available for a busy festive fixture schedule.
"I am delighted that we have probably got a bit of justice as it deserved to be turned around," Allardyce told West Ham's official website. "There was never any doubt in my mind. While you can say the foot was high, it was a genuine attempt and Carlton kept his eye on the ball. It's a really good outcome for us.
"The way he is playing at the moment, he would have been a massive loss for us. He's been outstanding up front for us since Andy Carroll got injured and we didn't want to miss a player of so much importance for these three very important games - Reading away, Norwich City at home and a big FA Cup third-round tie with Manchester United.
"To have experienced Premier League players available is always very important at this time of year. This is the tough time mentally for players, as well as physically, but the mental side has to be the strongest to get some results. To have him back and available is a big boost for us."