The governing International Automobile Federation (FIA) said in a statement that its court of appeal has decided to reduce the sanction imposed on the French team to a reprimand and $50,000 fine.
The ban, handed out by stewards at last month's Hungarian Grand Prix [ Images ], would have prevented double world champion Alonso from appearing before his home crowd in Sunday's European Grand Prix.
Renault, who had argued the suspension would also have "severe consequences" for local organisers as well as hitting fans who had bought tickets in the expectation of Alonso racing, welcomed the decision.
"The team acknowledges sporting regulations were breached during the incident in the pit lane of the Hungarian Grand Prix, which compromised safety," Renault said in a separate statement.
"The team therefore accepts the decision of the FIA to issue a reprimand and a $50,000 fine is fair and balanced."
Stewards had punished Renault for allowing Alonso to rejoin the race after a pitstop despite allegedly knowing his car's right front wheel was not properly attached. The wheel came off shortly afterwards.
It also followed the death of Henry Surtees [ Images ] in a Formula Two race at Brands Hatch after the 18-year-old Briton, son of 1964 world champion John, was hit on the head by a loose wheel bouncing across the track.
The team admitted a breach of regulations but denied deliberate misconduct, with Renault lawyer Ali Malek telling the four appeal court judges the punishment was excessive and unfair.
"This case does not deserve more than a reprimand," he added. "Was there conscious wrongdoing from Renault? There was none whatsoever.
"The only persons who knew ... were the two mechanics," added Malek. "Nobody on the pitwall knew there was a problem and the driver did not know either.
"There was a series of unfortunate events but no conscious wrongdoing."
Renault, who said the mechanics were not able to inform colleagues on the pitwall before the wheel bounced off the car, had been confident their appeal would be upheld.
"I've been optimistic ever since we got the penalty. We feel the penalty is unjust. We admit we did some stuff wrong but we don't think the penalty fits the crime," team manager Steve Nielsen had told reporters after the hearing.
While Alonso is sure to race, Renault have yet to confirm who will be his team mate after an acrimonious separation from Brazilian Nelson Piquet following the race in Budapest.
The team's Swiss-born test driver Romain Grosjean, who competed under a French licence, has been widely tipped to get the vacant position.