The Scottish Premiership side were eliminated from the competition at the qualifying stages by the Polish outfit over two legs.
But Ronny Deila has been handed a lifeline after a clerical error, and Celtic will enter the pot for the play-off round.
The Polish side brought on suspended player Bartosza Bereszynski with four minutes left to go in their 2-0 second-leg win over the Scottish champions.
Uefa's rules state that a side found guilty of fielding an ineligible player will forfeit the match 3-0 which means that the 6-1 aggregate win for Legia Warsaw is changed to a 4-4 draw, with Celtic winning on away goals.
While Legia can appeal Uefa's decision, it will be Celtic who are included in Friday's Champions League draw as a seeded team.
Bereszynski was banned for three games after receiving a red card in the Europa League last term and his absence from both legs against St Patrick's Athletic and the first leg against Ronny Deila's side meant Legia believed he was eligible to play at Murrayfield on Wednesday. However, their failure in registering him as part of the squad for the matches against the Irish side which meant the ban was not fulfilled.
Uefa released a statement on Friday to confirm that Celtic have been reinstated into the competition.
"The Uefa Control, Ethics and Disciplinary Body has met today and announced the following disciplinary decision following the 2014/15 Uefa Champions League third qualifying round tie in Edinburgh between Celtic FC and Legia Warszawa on 6 August 2014," the statement read.
"Legia have been sanctioned for fielding an ineligible player (article 18 of the Uefa Champions League regulations and article 21 of the Disciplinary Regulations). The match has been declared as forfeit meaning Legia Warszawa have lost the match 3-0.
"As a consequence, Celtic have qualified for the Uefa Champions League play-offs on away goals (agg: 4-4) and Legia will compete in the Uefa Europa League play-offs.
"In addition the player Bartosz Bereszynski has been suspended for one additional Uefa competition match for which he would be otherwise eligible.
"This suspension shall be added to the remaining two match suspension which the player still has to serve in accordance with the Control and Disciplinary Body decision of 13 February 2014."