Luitz stunned Austrian favourite Marcel Hirscher to claim his maiden World Cup victory in December but the International Skiing Federation (FIS) disqualified him for using supplemental oxygen between the first and second runs.
The 26-year-old was photographed inhaling oxygen from a mouthpiece in the hospitality area.
The use of oxygen does not constitute a prohibited method for World Anti-Doping Agency WADA but FIS bans it during competitions.
However, the Court of Arbitration for Sport (CAS) decided on Friday that the FIS rule was in conflict with the World Anti-Doping Code (WDC) and that the latter took priority.
"The athlete's appeal against the FIS Doping Panel decision has been upheld," CAS said.
"Stefan Luitz is no longer disqualified from the giant slalom at....Beaver Creek on Dec 2, 2018, and the order that he forfeit any medals, points and prizes obtained at such event is revoked."
The decision will not affect the overall World Cup title or the season giant slalom title, both of which were won by Hirscher.
(Reporting by Brian Homewood, editing by Ed Osmond)
