The Swiss club were thrown out of the tournament on September 2nd after being found guilty of fielding ineligible players, with the Scottish club handed their place in the group stages despite losing the play-offs 3-1 on aggregate.
Sion had vowed to fight their expulsion but lost their appeal to be reinstated during a UEFA hearing on Tuesday.
A UEFA statement confirmed: "THE UEFA Appeals Body today rejected FC Sion's appeal against their expulsion from the group stages of this season's Europa League."
Sion has up to 10 days within receipt of the written grounds of UEFA's decision to file an appeal with the Court of Arbitration for Sport (CAS) in Lausanne.
UEFA's statement continued: "The Appeals Body heard the parties and decided to reject the appeal lodged by FC Sion, confirming that the Swiss club had fielded ineligible players in both ties."
UEFA said Celtic will therefore play Club Atletico de Madrid on September 15th.
Earlier on Tuesday, a Swiss regional court backed Sion's fight to be reinstated in the competition.
"The civil court has this morning ordered UEFA to admit FC Sion as a participant of the UEFA Europa League 2011-2012 and to take all necessary measures to integrate it in the UEFA Europa League group in which FC Sion has qualified," Sion said in a statement.
"The Canton de Vaud Tribune also orders UEFA to consider the players Stefan Glarner, Billy Ketkeophomphone, Mario Mutsch, Pascal Feindouno, Jose Goncalves and Gabri as eligible as FC Sion players and to admit them in the 2011-12 UEFA Europa League.
"The order has been declared immediately binding."
But UEFA added: "UEFA also received today on this matter a court decision from the Tribunal Cantonal de Vaud and will issue a statement in this respect at a later stage."
News of the ruling was welcomed by the Scottish club: "Clearly, Celtic are pleased with the decision."
Celtic are currently preparing for the game in Spain but Sion president Christian Constantin has said his side also intend to travel to the Spanish capital.