Celtic will meet Maribor in the Champions League play-off round after the Court of Arbitration for Sport (Cas) rejected Legia Warsaw's bid to be provisionally reinstated.
Legia beat Celtic 6-1 in the third qualifying round but Uefa punished them for fielding a suspended player.
It meant their 2-0 second-leg win was overturned to 3-0 in Celtic's favour.
Cas has denied Legia's appeal for "provisional measures" to be taken, but will continue to arbitrate on the case.
It means Celtic manager Ronny Deila can now focus fully on the two-legged Champions League play-off against Slovenia's Maribor on Wednesday and next Tuesday.
Meanwhile, Legia Warsaw drop into the Europa League, where they will play Aktobe in Kazakhstan on Thursday.
The Polish champions beat Celtic 4-1 in Warsaw and 2-0 away.
But European governing body Uefa awarded the second-leg 3-0 to Celtic because Legia had fielded suspended player Bartosz Bereszynski for the last few minutes at Murrayfield.
That made the aggregate score 4-4 and Celtic went through on the away goals rule.
The Poles were upset because they thought Bereszynski had already served his three-match ban for violent conduct, picked up in Legia's last Europa League group match last season.
They did not play him in either leg of the previous qualifying round against St Patrick's this season, or in the first leg of the game against Celtic.
But, in fact, the player had not been registered for the previous round and thus his three-match ban had not been fully served by the time he played against Celtic.
A statement issued by Cas on Monday read: "The president of the Cas appeals arbitration division considered the parties' written submissions and has denied Legia Warszawa's request.
"Accordingly, Celtic FC remains qualified to participate in the Uefa Champions League 2014-2015 and will play its next match against NK Maribor on 20 August 2014.
"The Cas arbitration will now continue and a panel of arbitrators will be constituted to examine this case within the next week."
On submitting their case to Cas, Legia had stated: "We believe that Cas will investigate the case mainly on the level of rationality and proportionality of the decisions of Uefa disciplinary body and the spirit of the game. We still hope that finally football and fair play will win."
They expected that, had Cas decided they had a case worthy of further investigation, that it would expect it to be concluded "within the regular period of three months".