Celtic’s Champions League reprieve earned them a clash with Slovenian champions Maribor in the final play-off round.
The Scottish league winners were beaten 6-1 on aggregate by Legia Warsaw in the previous round but the Poles were punished for fielding an ineligible player.
Bartosz Bereszynski, who came on as an 86th-minute substitute as Legia won the second leg 2-0 at Murrayfield on Wednesday night, was suspended following a red card for violent conduct in last season’s Europa League.
Hours before the draw for the next round was to be made, Uefa announced that Celtic had been awarded a 3-0 win in the second leg, and therefore qualified on away goals after a 4-4 aggregate result.
Celtic reached the group stages last season but failed to progress from an extremely tough pool that also included AC Milan, Barcelona and Ajax.
Arsenal will meet Turkish side Besiktas in the two-legged play-off.
Arsene Wenger’s side, who finished fourth in the Premier League last season, will travel to Istanbul for the first match in the week beginning August 18th, with the home leg taking place the following week.
Arsenal have never previously met Besiktas in any European competition.
Ronny Deila admits Celtic's dramatic reinstatement has left him feeling "very strange."
Speaking at the club’s Lennoxtown training complex the Celtic manager said: “It is very strange, I have to say that.
“First of all I feel very sorry for Legia, and my friends from Norway there.
“It is tough to think of that and now we are in the Champions League.
“That is what Uefa said, we haven’t been involved in anything.
“I am a football manager and I have to go with it and now we are preparing for Maribor.”
Tottenham will face Cypriot side AEL Limassol in the final play-off round of the Europa League.
Mauricio Pochettino’s first European match in charge of Spurs will come in Cyprus on August 21st, with Limassol travelling to London the following Thursday.
Last season Tottenham made it through the group stages but were eliminated by eventual runners-up Benfica in the last 16.
Hull’s reward for a narrow win over Slovakian’s AS Trencin in the previous round is a tie against Belgians Lokeren.
The Tigers’ European adventure looked like it would end at the first hurdle thanks to Trencin’s away goal in Thursday night’s second leg at the KC Stadium but Sone Aluko netted a winner 10 minutes from time.
Lokeren, who will host the first leg, were beaten at the same stage last season by Czech side Viktoria Plzen.
Legia Warsaw will meet Kazakh side FC Aktobe.
Champions League play-off draw
Maribor v Celtic
SV Red Bull Salzburg v Malmo
AaB v APOEL Nicosia
Steaua Bucuresti v Ludogorets
Slovan Bratislava v BATE
Besiktas v Arsenal
Standard Liege v Zenit St. Petersburg
FC Copenhagen v Bayer Leverkusen
Lille v FC Porto
Napoli v Athletic Bilbao
Europa League play-off draw
FK Sarajevo v Borussia M’gladbach
Astana v Villarreal
Apollon Limassol v Lokomotiv Moscow
PEC Zwolle v Sparta Prague
Young Boys v Debrecen
Asteras Tripoli v Maccabi Tel-Aviv
FC Spartak Trnava v FC Zurich
AEL v Tottenham Hotspur
Dnipro v Hajduk Split
Dinamo Minsk v Nacional
Karabakh v FC Twente
Petrolul Ploiesti v Dinamo Zagreb
HJK Helsinki v Rapid Vienna
Trabzonspor v Rostov
FC Zimbru v PAOK
RNK Split v Torino
Omonia Nicosia v Dinamo Moscow
Aktobe v Legia Warsaw
Lyon v Astra Giurgiu
Lokeren v Hull
Neftchi v Partizan Belgrade
Ruch Chorzow v Metalist Kharkiv
IF Elfsborg v Rio Ave
PSV v Shakhtyor
Karabukspor v St Etienne
Stjarnan v Inter Milan
Panathinaikos v FC Midtjylland
Feyenoord v Zarya Luhansk
Grasshoppers v Club Brugge
Real Sociedad v Krasnodar
Rijeka v FC Sheriff