Dundalk can look forward to a trip to London after being paired against Arsenal in the Europa League group phase.
The Irish side secured their place with a victory over Faroese side KI Klaksvik in the final qualifying round, and will now face the Gunners home and away in Group B.
The other two sides in the group are Austrian club Rapid Vienna and Molde from Norway.
Tottenham have been drawn alongside Ludogorets, LASK and Royal Antwerp in Europa League group J.
Celtic and Rangers were drawn against sides with great European pedigree, with the Hoops facing seven-times European Cup winners AC Milan and the Light Blues taking on two-time champions of Europe Benfica from Portugal.
Celtic, who were losing UEFA Cup finalists in 2003, will also face Czech side Sparta Prague and French club Lille in Group H.
Neil Lennon's side dropped into the Europa League qualifiers after being knocked out of the 2020-21 Champions League by Ferencvaros of Hungary.
Rangers will face Standard Liege of Belgium and Polish side Lech Poznan in Group D, in addition to the glamour trip to Lisbon.
The Europa League 2020-21 group stage draw in full
Group A
Roma (Italy), Young Boys (Switzerland), Cluj (Romania), CSKA Sofia (Bulgaria)
Group B
Arsenal (England), Rapid Vienna (Austria), Molde (Norway), Dundalk (Ireland)
Group C
Bayer Leverkusen (Germany), Slavia Prague (Czech Republic), Hapoel Beer-Sheva (Israel), Nice (France)
Group D
Benfica (Portugal), Standard Liege (Belgium), Rangers (Scotland), Lech Poznan (Poland)
Group E
PSV Eindhoven (Netherlands), PAOK Thessaloniki (Greece), Granada (Spain), Omonia (Cyprus)
Group F
Napoli (Italy), Real Sociedad (Spain), AZ Alkmaar (Netherlands), Rijeka (Croatia)
Group G
Braga (Portugal), Leicester (England), AEK Athens (Greece), Zorya Luhansk (Ukraine)
Group H
Celtic (Scotland), Sparta Prague (Czech Republic), AC Milan (Italy), Lille (France)
Group I
Villarreal (Spain), Qarabag (Azerbaijan), Maccabi Tel-Aviv (Israel), Sivasspor (Turkey)
Group J
Tottenham (England), Ludogorets Razgrad (Bulgaria), LASK (Austria), Royal Antwerp (Belgium)
Group K
CSKA Moscow (Russia), Dinamo Zagreb (Croatia), Feyenoord (Netherlands), Wolfsberger (Austria)
Group L
Gent (Belgium), Red Star Belgrade (Serbia), Hoffenheim (Germany), Slovan Liberec (Czech Republic)
