UEFA have rejected Sion's appeal to re-enter Udinese's Europa League group, so Celtic maintain their place.
The Swiss side had originally won the play-off against Celtic to enter the competition, but were thrown out on September 2 for fielding ineligible players.
A Swiss regional court backed Sion's legal battle to be reinstated, but UEFA have formally rejected that appeal.
“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,” said a statement on uefa.com.
“As a consequence, Celtic FC remain qualified for the UEFA Europa League group stage and will play against Club Atlético de Madrid on Thursday 15 September.
“An appeal against this decision can be lodged to the court of arbitration for sport within 10 days of receipt of the written grounds for the decisions.”
Sion President Christian Constantin claimed the team would travel to Madrid for Thursday's game despite the response.
The other team in Group I is French side Rennes, who play Udinese on Thursday.