The game's governing body ruled the Polish champions fielded full-back Bartosz Bereszynski for the final three minutes of their 2-0 victory at Murrayfield, a result which earned them a 6-1 aggregate win, despite him not being registered.
UEFA's investigation centred on Bereszynski's sending-off for violent conduct against Apollon in the final match of Legia's Europa League campaign last season.
He missed both ties against St Patrick's in the second qualifying round and then sat out the first leg against Celtic.
But UEFA decided he had not been registered in Legia's squad for the games against the Irish side in order to allow a three-match suspension to take effect.
In a statement, UEFA said: "The UEFA Control, Ethics and Disciplinary Body have announced that Legia have been sanctioned for fielding an ineligible player in their second leg against Celtic.
"The match has been declared as forfeit and Legia have lost the match 3-0. As a consequence, Celtic have qualified for the 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."
Legia chairman Boguslaw Lesniodorski reacted by saying that he hoped Celtic will not accept UEFA's decision.
Lesniodorski told Sky Sports News: “I’m very disappointed, once again football and sport lost. We hope that Celtic will react and follow fair play rules. For us what happened on the field matters.”
Legia offical Dominik Ebebenge added: "This is unjust and completely disproportionate. There have been similar cases in the past which have not been punished in this way.
"This is just basic human error. We have spent eight years working towards this and now it has bene taken away from us. Financially, it's unimaginable and the players are shattered. "
In the draw which followed the ruling, Celtic were paired with Maribor of Slovenia for a place in the group stages of the competition.
What a farce. The player only played for two minutes, was it really worth it! Also very funny that Celtic still only just scraped through on away goals, despite being awarded a 3-0 win. This confirms that the Scottish league is of a terrible standard, if indeed it needed confirming which it probably didn't... #LOLZ- jegz1uk