Milan were the last of the 48 teams to reach the group stage after a wild, 24-penalty shootout in Portugal against Rio Ave.
In the rain-swept shootout, three Rio Ave players failed even to get on target with penalties that could have won the match. Milan goalkeeper Gianluigi Donnarumma later made a decisive save that led to the victory.
Milan, who last won the Champions League in 2007, came from the pot of third-seeded teams. Scottish champions Celtic were the top-seeded team.
Arsenal, the Europa League runner-up in 2019, are the highest-ranked team in the competition and were grouped with Rapid Vienna, Molde and Dundalk. North London rivals Tottenham will face LASK, Ludogorets Razgrad and Royal Antwerp.
Roma are the top-seeded team in a group with two clubs that started the season in the Champions League -- Young Boys and Cluj. CSKA Sofia are also in that group.
Spanish club Villarreal face the most demanding travel schedule, facing Azeri club Qarabag, Israeli team Maccabi Tel-Aviv and Turkish club Sivasspor.
The group stage begins on Oct. 22 and runs until Dec. 10. UEFA said last week that games postponed because of the coronavirus pandemic can be made up until Jan. 28.
Games can be moved to a neutral country if virus cases or travel restrictions prevent the home team from hosting or the away team from travelling to the original venue. Home fans can attend games at up to 30% of a stadium's capacity with approval from domestic public authorities, UEFA said on Thursday. No tickets will go to the away teams.
Ahead of the draw ceremony at UEFA headquarters, Inter Milan forward Romelu Lukaku was named the best player in the Europa League last season. Lukaku scored seven goals in six games, including in the 3-2 loss to Sevilla in the final.