Liverpool will face German side Hoffenheim for a place in the Champions League group stage.
Jurgen Klopp's side will be away for the first leg on either 15 or 16 August, with the return leg to be played at Anfield on 22 or 23 August.
Scottish champions Celtic meet Kazakh counterparts Astana in their play-off tie, with the home leg first.
Everton host Croatia's Hajduk Split in the Europa League play-off first leg on 17 August with the return on 24 August.
The Toffees qualified by securing a 2-0 aggregate win over MFK Ruzomberok on Thursday.
The 10 winners from the Champions League play-off stage will join the 22 teams who have already qualified for the group stage.
Defeated teams at the play-off round enter the Europa League group stage.
Liverpool qualified for the Champions League play-off stage by finishing fourth in last year's Premier League, with Hoffenheim taking the same position in the Bundesliga.
Premier League champions Chelsea, runners-up Tottenham and third-placed Manchester City qualified directly for the group stage, along with Manchester United, who won last year's Europa League.
The 22 winners of the Europa League play-off round ties will qualify for the group stages.
Champions League draw
Qarabag (Azerbaijan) v Copenhagen (Denmark)
Apoel Nicosia (Cyprus) v Slavia Prague (Czech Republic)
Olympiakos (Greece) v HNK Rijeka (Croatia)
Celtic (Scotland) v Astana (Kazakhstan)
Hapoel Beer Sheva (Israel) v Maribor (Slovenia)
Istanbul Basaksehir (Turkey) v Sevilla (Spain)
Young Boys (Switzerland) v CSKA Moscow (Russia)
Napoli (Italy) v Nice (France)
Hoffenheim (Germany) v Liverpool (England)
Sporting Lisbon (Portugal) v Steaua Bucharest (Romania)
Europa League draw
Shkendija (Macedonia) v AC Milan (Italy)
Panathinaikos (Greece) v Athletic Bilbao (Spain)
Osijek (Croatia) v Austria Wien (Austria)
Apollon Limassol (Cyprus) v Midtjylland (Denmark)
Crvena Zvezda (Serbia) v Krasnodar (Russia)
FH (Iceland) v Braga (Portugal)
Club Brugge (Belgium) v AEK Athens (Greece)
Everton (England) v Hajduk Split (Croatia)
Viitorul (Romania) v Salzburg (Austria)
Vardar (Macedonia) v Fenerbahce (Turkey)
Maritimo (Portugal) v Dynamo Kiev (Ukraine)
Partizan (Serbia) v Videoton (Hungary)
Ajax (Netherlands) v Rosenborg (Norway)
Altach (Austria) v Maccabi Tel Aviv (Israel)
Legia Warsaw (Poland) v Sheriff Tiraspol (Moldova)
Utrecht (Netherlands) v Zenit St Petersburg (Russia)
BATE Borisov (Bulgaria) v Olexandriya (Ukraine)
Viktoria Plzen (Czech Republic) v Larnaca (Cyprus)
PAOK (Greece) v Ostersund (Sweden)
Domzale (Slovenia) v Marseille (France)
Dinamo Zagreb (Croatia) v Skenderbeu (Albania)
Ludogorets (Bulgaria) v Suduva (Lithuania)