Soucek was shown a straight red card by referee Mike Dean in second half stoppage time after he appeared to accidentally catch Aleksandar Mitrovic in the face with his elbow as the pair jostled for a free kick.
Dean was invited to consult his pitch side monitor to review the incident and promptly sent the 25-year-old Czech Republic international off.
Soucek, who has been one of West Ham’s most important players with eight goals in the top flight, would have missed games against Manchester United, Sheffield United and Tottenham Hotspur if the appeal was unsuccessful.
"Tomas Soucek will be available for West Ham United FC's next three fixtures following a successful claim of wrongful dismissal," an FA statement read on Monday.
"The midfielder was sent off during a Premier League fixture against Fulham FC on Saturday for violent conduct."
Upon hearing the good news, Soucek tweeted: "I am glad my red card against Fulham has been overturned."
"I've checked it, I've gone over 200 games without a single red card. My entire career.
"I am looking forward to helping the team in the important games this week! Thanks for your support!"
