Legia Warsaw knocked out the Scottish club 6-1 over two legs, but were kicked out of the competition for fielding an ineligible player.
The Polish club had their appeal to be demoted to the Europa League overturned by Uefa on Thursday.
Football's governing body issued a statement that read: "The appeal lodged by the Polish club was rejected and, therefore, the original decision of the Uefa Control, Ethics and Disciplinary Body is confirmed."
Legia are set to take their case to the Court of Arbitration for Sport (CAS), said the BBC.
Celtic will take the Polish club's place in the Champions League and play Maribor for a slot in group stage proper of the Champions League
Meanwhile Legia will face Kazakhstani side Aktobe in the Europa League.
Ronny Deila has strengthened his side ahead of the match against Maribor, signing Jason Denayer from Manchester City and Bulgarian Winger Aleksander Tonev from Aston Villa.
The Norwegian refused to comment on his side's re-entry to the Champions League.