Roma are paired with Borussia Monchengladbach in the Europa League group stage, while Lazio have a mini group of death with Celtic and Stade Rennais.
Roma were given a bye into the group stage after Milan pulled out of the competition and Torino took their place in the playoffs.
Capitalising on their Pot 1 status, they have been drawn Monchengladbach, Turkish side Istanbul Basaksehir and Austrian outfit Wolfsberger in Group J.
The Germans are back in Europe after a two-year absence, while Basaksehir bowed out of the Champions League at the third qualifying phase.
Wolfsberger, meanwhile, have qualified for the Europa League group stage for the first-ever time in their history.
Lazio, on the other hand, have been dealt a tough hand, with Scottish champions Celtic and Romanian title-holders CFR Clug standing in their way.
Group E is rounded off by Stade Rennais, who caught the eye last season as they came close to knocking out Arsenal, winning their last-16 first leg 3-1.
Elsewhere, Wolverhampton Wanderers – who eliminated Torino in the playoffs – are paired with Besiktas, Braga and Slovan Bratislava.
Finally, Paul Pogba’s Manchester United face a nine-hour flight to Kazakhstan, where they will take on Astana.
The group stage kicks off on September 19, with games to follow on October 3, October 24, November 7, November 28 and December 12.
Europa League 2019-20 groups in full
Group A :Sevilla, APOEL Nicosia, Qarabag, Dudelange
Group B: Dynamo Kiev, FC Copenhagen, Malmo, Lugano
Group C: Basel, Krasnodar, Getafe, Trabzonspor
Group D: Sporting CP, PSV, Rosenborg, LASK
Group E: Lazio, Celtic, Stade Rennais, CFR Cluj
Group F: Arsenal, Eintracht Frankfurt, Standard Liege, Vitoria Guimaraes
Group G: Porto, Young Boys, Feyenoord, Rangers
Group H: CSKA Moscow, Ludogorets, Espanyol, Ferencvaros
Group I: Wolfsburg, Gent, Saint-Etienne, Oleksandriya
Group J: Roma, Borussia Monchengladbach, Istanbul Basaksehir, Wolfsberger
Group K: Besiktas, Braga, Wolverhampton Wanderers, Slovan Bratislava
Group L: Manchester United, Astana, Partizan Belgrade, AZ
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