The Everton midfielder and West Ham striker 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 December 22 - play which was 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.
A statement from the FA read: “The FA can confirm that red cards shown to West Ham United's Carlton Cole and Everton's Darron Gibson have been rescinded.
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Hammers boss Sam Allardyce has expressed delight at the news that Cole will be available for a busy festive fixture schedule.
He told the club’s official website: "I am delighted that we have probably got a bit of justice as it deserved to be turned around. 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."