The Polish champions took their case to the Swiss-based court after UEFA's appeal committee elected last week not to overturn the governing body's original decision to punish them for fielding a suspended player in their third qualifying round tie against Ronny Deila's side.
The CAS, though, chose not to heed Legia's request to allow them back into the competition pending a wider enquiry, meaning Celtic will now face Maribor in the first leg of the play-off round tomorrow night. CAS will examine the case in further detail "within the next few weeks", with Legia seeking financial compensation from UEFA for their actions.
A CAS statement read: "The Court of Arbitration for Sport [CAS] has denied the urgent request for provisional measures filed by the Legia Warszawa SA in the course of its appeal against the UEFA Appeals Body decision of 13 August 2014.
"The UEFA Appeals Body had confirmed the result 3-0 [forfeit] in favour of Celtic FC against Legia in the second leg of the third qualifying round of the UEFA Champions League. UEFA considered that Legia had fielded an ineligible player [Bartosz Bereszynski] during the match.
"Legia Warszawa filed an appeal to the CAS at 17:30 on 15 August 2014 together with an urgent application for provisional measures requesting that it be provisionally admitted to participate in UEFA Champions League matches until the CAS renders its final arbitral award.
"The appeal is directed against UEFA and Celtic FC which were invited to comment on the Polish club's request until 13:00 [Swiss time] today.
"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 Champion's League 2014/2015 and will play its next match against NK Maribor on 20 August 2014."
Celtic, meanwhile, are expected to be joined for that first-leg tie in Slovenia by Rubin Kazan's Ghanaian midfielder Mubarak Wakaso.
The player's agents last night confirmed he was en route to Moscow to complete a medical this morning ahead of a loan move to the Scottish champions.
Derk Boerrigter will be banned for Celtic's forthcoming league games against Inverness Caledonian Thistle and Dundee after accepting the Scottish Football Associaton's offer of a two-match suspension for "causing a match official to make an incorrect decision by committing an act of simulation".
Boerrigter won Celtic a penalty, converted by Nir Biton, in the recent 3-0 win over St Johnstone at McDiarmid Park, although television evidence suggested there had been little contact from Dave Mackay who was sent off in the incident.
St Johnstone have appealed their captain's red card and a tribunal will convene on Thursday to discuss it.