Referee Mark Halsey sent off the England defender for serious foul play against Manchester City on Saturday.
Terry hauled down City striker Jo as he raced towards goal, using his arm to perform a pseudo-rugby tackle.
"At an Independent Regulatory Commission hearing today, a claim for wrongful dismissal from Chelsea's John Terry was upheld," said an FA statement.
"As a result of today's hearing, Terry's three match suspension has been withdrawn."
Halsey's designation of the offence as serious foul play, rather than a professional foul, indicated he did not believe Terry to be the last defender.
Chelsea argued successfully that the foul warranted no card as the FA are not empowered to downgrade cards from red to yellow, merely to strike them off altogether.
The news comes as a major boost to the Premier League leaders, who can count on Terry for the visit of champions United to Stamford Bridge on Sunday.
United are without a key defender in Nemanja Vidic, who was sent off for a second bookable offence in the 2-1 defeat at Liverpool on Saturday.
Midfielder Michael Carrick is also out after it was revealed he has a broken foot and could miss up to six weeks.
Chelsea's haul of 10 points from their first four games gives them a lead of six points over United, who have a game in hand.
