The Swiss club were thrown out of the tournament on September 2 after being found guilty of fielding ineligible players, with Celtic handed their place in the group stages despite losing the play-offs 3-1 on aggregate.
Sion vowed to fight their expulsion but have lost their appeal to be reinstated following Tuesday's hearing.
A UEFA statement confirmed: "THE UEFA Appeals Body today [Tuesday] rejected FC Sion's appeal against their expulsion from the group stages of this season's Europa League."
Sion can take their case to the Court of Arbitration for Sport within 10 days of written receipt of Tuesday's decision.
However, Celtic look set to face Atletico Madrid in Thursday night's opening game, despite Sion president Christian Constantin claiming his side also plan to travel to the Spanish capital.
UEFA's statement in full read: "The UEFA Appeals Body today [Tuesday] dealt with the appeal lodged by FC Sion against the decision of the UEFA Control and Disciplinary Body of 02 September to forfeit their two UEFA Europa League play-off ties played against Celtic FC on 18 and 25 August.
"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.
"As a consequence, Celtic FC remain qualified for the UEFA Europa League group stage and will play against Club Atletico de Madrid on Thursday 15 September.
"An appeal against this decision can be lodged to the Court of Arbitration for Sport within ten days of receipt of the written grounds for the decisions."
Earlier on Tuesday, a Swiss regional court backed Sion's fight to be reinstated in the competition.
The UEFA statement added: "UEFA also received today [Tuesday] 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 Tuesday's ruling was welcomed by Celtic, who now face a tough challenge in the group stages.
A statement from the club read: "The UEFA Appeals Body today [Tuesday] rejected FC Sion's appeal against their expulsion from the group stages of this season's Europa League.
"Celtic were reinstated to the competition, and will take on Atletico Madrid, Udinese and Rennes. The first match takes place this Thursday, September 15 at the Vicente Calderon Stadium in Madrid.
"Clearly, Celtic are pleased with the decision."
Sion's struggle to be reinstated is not the only controversy surrounding Thursday's tie as Celtic prepare to face old foes.
Former Celtic captain and manager Billy McNeill last week described Atletico as "scum" in reference to their elimination from the 1974 European Cup semi-finals at the hands of the Spaniards.
Atletico had three men sent off and seven booked in an infamous goalless first leg at Celtic Park before winning in Madrid.
Jimmy Johnstone was subjected to particularly brutal treatment and the match ended with a tunnel brawl.
Celtic chief executive Peter Lawwell tonight attempted to ease tensions ahead of the game. The last time a Scottish club played at the Vicente Calderon Stadium was in November 2007 when Aberdeen complained to UEFA after a number of their fans were injured in disturbances with home fans and police.
Lawwell told www.celticfc.net: "A lot has been said about previous meetings between the clubs and we absolutely understand that passions can run very high, but regardless of what has happened historically, we now have a responsibility to ensure that Thursday evening is a celebration of football.
"We are in a new era and we enjoy good sporting relations between the clubs. We have full respect for Atletico Madrid, the team, and those who manage the club.
"On Thursday, we hope both sets of supporters enjoy the occasion and we are sure that Celtic supporters will do what they always do and continue to uphold the great name and reputation that they have earned.
"Our fans have travelled to many cities across Europe over many decades and I know they go with the intention of enjoying the event.
"We are proud to be travelling to Madrid, one of the world's great cities, to play one of Spain's major football clubs.
"We know our supporters will be looking forward to this match with great anticipation and will provide the team with their customary positive backing."
Celtic manager Neil Lennon added: "Ever since joining Celtic, it has been an absolute privilege to be in European competition backed by our magnificent support.
"Our fans have shown time and time again how to back their club positively, how to make new friends and enjoy some great footballing occasions, particularly across Spain in Seville and Villarreal.
"This is something which has been recognised by both UEFA and FIFA.
"We know our fans will want to go to Madrid on Thursday with the intention of enjoying the match in a great European city."