The Polish side were punished by UEFA for fielding an ineligible player in their 6-1 aggregate win over Celtic in the third qualifying round of European football's elite club competition.
Legia appealed UEFA's decision to award Celtic a 3-0 third qualifying round second-leg win which saw the Scottish champions progress to the play-offs on away goals, but on Thursday the organisation's appeals body upheld the decision, prompting Legia to ask CAS to intervene.
Legia failed to submit the prompt appeal to CAS they had promised, but the club confirmed late on Friday night they had indeed sought arbitration from the Switzerland-based organisation.
A statement on Legia's website said: "Legia Warsaw announces that today an appeal has been submitted to the Court of Arbitration for Sport in Lausanne (CAS) against the decision of the UEFA Appeals Committee of 13 August 2014."
CAS confirmed it had received Legia's appeal, saying: "The Court of Arbitration for Sport registered today at 17:30 a statement of appeal filed by the Polish club Legia Warsaw 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 18 August around 18:00 (Swiss time)."
The punishment, which turned a 6-1 aggregate win for Legia into an away-goals defeat, stemmed from Legia's failure to register Bereszynski in their squad list for the second qualifying round against St Patrick's.
That meant his three-match suspension had not officially been served when he came on as an 86th-minute substitute as Legia beat Celtic 2-0 at Murrayfield.
As things stand, Celtic are due to play Slovenian side Maribor for a place in the Champions League group stages next Wednesday, while Legia will face Kazakhstan side Aktobe in a Europa League qualifier the following day.