Arsenal will play Turkish side Besiktas in the Champions League play-off round, while Celtic face Slovenian champions Maribor after being reinstated.
The Gunners have appeared in the group stages of the Champions League in each of the past 16 seasons.
Celtic lost 6-1 to Legia Warsaw in qualifying, but the Polish champions fielded an ineligible player.
In the Europa League, Tottenham will play AEL Limassol of Cyprus and Hull City face Belgian side Lokeren.
Besiktas finished third in the Turkish Super League, are managed by former West Ham and Everton defender Slaven Bilic and their squad includes striker Demba Ba, who moved from Chelsea in July.
Scottish champions Celtic will play Maribor in a two-legged match with the winners advancing into the main Champions League group stage.
It is a second chance for the Bhoys after they lost 4-1 in the first leg of their third qualifying round tie in Poland, and 2-0 at home in the second leg on Wednesday.
However, Legia defender Bartosz Bereszynski came on a substitute for the final two minutes of the second leg.
He was sent off against Apollon in the final match of Legia's Europa League campaign last season, earning a three-match suspension.
The club failed to register Bereszynski for both legs of Legia's tie against St Patrick's Athletic in the second qualifying round, so therefore he was still suspended for both games against Celtic.
|Champions League play-off round|
|Maribor (Slovenia) v Celtic (Scotland)|
|Salzburg (Austria) v Malmo (Sweden)|
|Aalborg (Denmark) v Apoel Nicosia (Cyprus)|
|Steaua Bucharest (Romania) v Ludogorets (Bulgaria)|
|Slovan Bratislava (Slovakia) v BATE Borisov (Belarus)|
|Besiktas (Turkey) v Arsenal (England)|
|Standard Liege (Belgium) v Zenit St Petersburg (Russia)|
|FC Copenhagen (Denmark) v Bayer Leverkusen (Germany)|
|Lille (France) v Porto (Portugal)|
|Napoli (Italy) v Athletic Bilbao (Spain)|
For Arsenal, it is the second successive season they will have faced Istanbul opposition at this stage, after they beat Fenerbahce 5-0 on aggregate last year.
The first legs will take place on either 19 or 20 August with the second legs a week later.
Premier League champions Manchester City, Liverpool and Chelsea have already secured their place in the group stage.
FA Cup finalists Hull, playing in European competition for the first time, beat Trencin of Sloavkia 2-1 on aggregate in the third qualifying round of the Europa League.
The first legs of the Europa League play-offs will be played on Thursday, 21 August and the second legs on 28 August.
Hull and Tottenham will be hoping to join Everton in the group stage.
|Europa League play-off round|
|FK Sarajevo (Bosnia-Hercegovina) v Borussia Monchengladbach (Germany)|
|Astana (Kazakhstan) v Villarreal (Spain)|
|Apollon Limassol (Cyprus) v Lokomotiv Moscow (Russia)|
|PEC Zwolle (Netherlands) v Sparta Prague (Czech Republic)|
|Young Boys (Switzerland) v Debrecen (Hungary)|
|Asteras Tripoli (Greece) v Maccabi Tel-Aviv (Israel)|
|FC Spartak Trnava (Slovakia) v FC Zurich (Switzerland)|
|AEL Limassol (Cyprus) v Tottenham Hotspur (England)|
|Dnipro (Ukraine) v Hajduk Split (Croatia)|
|Dinamo Minsk (Belarus) v Nacional (Portugal)|
|Karabakh (Azerbaijan) v FC Twente (Netherlands)|
|Petrolul Ploiesti (Romania) v Dinamo Zagreb (Croatia)|
|HJK Helsinki (Finland) v Rapid Vienna (Austria)|
|Trabzonspor (Turkey) v Rostov (Russia)|
|FC Zimbru (Moldova) v PAOK (Greece)|
|RNK Split (Croatia) v Torino (Italy)|
|Omonia Nicosia (Cyprus) v Dinamo Moscow (Russia)|
|Aktobe (Kazakhstan) v Legia Warsaw (Poland)|
|Lyon (France) v Astra Giurgiu (Romania)|
|Lokeren (Belgium) v Hull (England)|
|Neftchi (Azerbaijan) v Partizan Belgrade (Serbia)|
|Ruch Chorzow (Poland) v Metalist Kharkiv (Ukraine)|
|IF Elfsborg (Sweden) v Rio Ave (Portugal)|
|PSV Eindhoven (Netherlands) v Shakhtyor (Belarus)|
|Karabukspor (Turkey) v St Etienne (France)|
|Stjarnan (Iceland) v Inter Milan (Italy)|
|Panathinaikos (Greece) v FC Midtjylland (Denmark)|
|Feyenoord (Netherlands) v Zarya Luhansk (Ukraine)|
|Grasshoppers (Switzerland) v Club Brugge (Belgium)|
|Real Sociedad (Spain) v Krasnodar (Russia)|
|Rijeka (Croatia) v FC Sheriff (Moldova)|