FA Cup winners Arsenal will face League of Ireland side Dundalk, Rapid Vienna and Molde in Group B of the 2020-21 Europa League.
Tottenham have been drawn alongside Bulgarian champions Ludogorets, LASK and Royal Antwerp in Group J.
Leicester City will face Braga, AEK Athens and Ukrainian side Zorya Luhansk in Group G.
Scottish champions Celtic face a tough task in Group H as they take on AC Milan, Lille and Sparta Prague.
Rangers are in Group D alongside Benfica, Standard Liege and Lech Poznan.
The first three group matches will take place on successive Thursdays from 22 October.
Arsenal qualified for the group stage by beating Chelsea to win their record 14th FA Cup in August. The Gunners lost to Chelsea in the 2019 Europa League final.
Dundalk beat Faroe Islands club KI Klaksvik on Thursday to secure their spot, while Austrian side Rapid Vienna were eliminated from the Champions League third qualifying round.
Tottenham, two-time winners of the preceding Uefa Cup, beat Maccabi Haifa in the play-off round, while Leicester were beaten to a top-four place on final day of the 2019-20 Premier League season to end up in the Europa League.
Celtic beat Bosnian side FK Sarajevo on Thursday to qualify and Rangers progressed against Turkish giants Galatasaray.
CSKA Moscow, who won the 2005 Uefa Cup, are in Group K along with fellow former winners Feyenoord, Croatia’s Dinamo Zagreb and Wolfsberger of Austria.
Napoli, the 1989 champions, face Real Sociedad, AZ Alkmaar and Croatian club Rijeka in Group F.
Bayer Leverkusen, who won in 1988, play Slavia Prague, Hapoel Beer-Sheva and Nice in Group C, while 1978 winners PSV Eindhoven take on Paok, Granada and Cypriot club Omonia in Group E.
Draw in full
Group A: Roma, Young Boys, Cluj, CSKA Sofia
Group B: Arsenal, Rapid Vienna, Molde, Dundalk
Group C: Bayer Leverkusen, Slavia Prague, Hapoel Beer-Sheva, Nice
Group D: Benfica, Standard Liege, Rangers, Lech Poznan
Group E: PSV Eindhoven, Paok Thessaloniki, Granada, Omonia
Group F: Napoli, Real Sociedad, AZ Alkmaar, Rijeka
Group G: Braga, Leicester, AEK Athens, Zorya Luhansk
Group H: Celtic, Sparta Prague, AC Milan, Lille
Group I: Villarreal, Qarabag, Maccabi Tel-Aviv, Sivasspor
Group J: Tottenham, Ludogorets, ASK Linz, Royal Antwerp
Group K: CSKA Moscow, Dinamo Zagreb, Feyenoord, Wolfsberg
Group L: Gent, Red Star Belgrade, Hoffenheim, Slovan Liberec
