The Polish side beat Celtic 6-1 on aggregate in the third qualifying round but were found to have used an ineligible player, Bartosz Bereszynski, as a late substitute in the second leg.
Celtic were awarded a 3-0 win by default for that match, putting them through on away goals to the playoff round, the first-leg of which is due to take place against Slovenian side Maribor on Wednesday.
Last Thursday UEFA's appeals body upheld the decision by its disciplinary body to award Celtic the 3-0 second-leg win.
Legia immediately indicated their intention to take their case further but appeared to have missed out when it was revealed they had failed to lodge the appeal by the end of business on Friday.
However, in a statement CAS said: "The Court of Arbitration for Sport registered today (Friday) at 17:30 a statement of appeal filed by the Polish club Legia Warszawa against the decision of the UEFA appeals body confirming 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.
"The UEFA considered that Legia had fielded an ineligible player (Bartosz Bereszynski) during the match.
"Legia requests urgent provisional measures from CAS allowing the Polish club to participate in the play-offs of the Champions League (20 & 26 August 2014).
"More generally, the club requests that the UEFA decision be set aside and that all sanctions against the club and the player Bereszynski be annulled.
"The CAS has immediately initiated an arbitration procedure and the respondents UEFA and Celtic FC have been invited to file written observations. A decision on request for provisional measures is likely to be issued on Monday August 18 around 18:00 (Swiss time)."