Lewis-Skelly was sent off by referee Michael Oliver in the first half of the Gunners' 1-0 win at Molineux following a challenge on Wolves defender Matt Doherty.
Darren England, the game's video assistant referee, supported Oliver's decision to dismiss the 18-year-old for serious foul play.
"An independent regulatory commission has upheld a claim of wrongful dismissal in relation to Myles Lewis-Skelly and removed his three-match suspension," a statement from the FA read on Tuesday.
"The Arsenal player was sent off for serious foul play during their Premier League fixture against Wolverhampton Wanderers on Saturday, January 25, 2025."
Arsenal's success in appealing means Lewis-Skelly will be available for Premier League games against Manchester City and Leicester and the second leg of their EFL Cup semi-final at Newcastle.