Arsenal have been drawn against Swedish club Ostersunds FK in the Europa League round of 32, while Atletico Madrid take on Copenhagen.
Arsenal, who secured top spot in their Europa League group, are still seeking their first European trophy under Arsene Wenger and will be confident of progress.
Ostersund will be in the midst of preseason when the tie takes place in February, with the Allsvenskan only getting underway in April, but their English coach Graham Potter told his club's official website he thinks it is a "fantastic draw."
He said: "I really wanted one of the big teams. I think it's really cool to get to go home to England and face one of the best teams in the Premier League. Now we're truly underdogs."
Diego Simeone's Atletico, who reached the Champions League final in both 2014 and 2016, enter the competition after unexpectedly finishing third behind Roma and Chelsea in their Champions League group.
They face Danish club Copenhagen as their first Europa League fixture as they seek a repeat of their successes in the competition in 2010 and 2012.
Atletico representative Clemente Villaverde said on UEFA's website: "We know them; we've played them before [a 2-0 win in 2007]. It's a good trip to go on and they'll make life difficult for us.
"We're happy to be back in the competition and that the final is in Lyon -- that brings happy memories given the city owes us one [Atletico lost 3-0 to Dynamo Kiev in Lyon in the 1986 Cup Winners' Cup final]."
— UEFA Europa League (@EuropaLeague) December 11, 2017
AC Milan, now under coach Gennaro Gattuso, play Bulgarian club Ludogorets Razgrad who made it through a group that included Braga, Istanbul Basaksehir and Hoffenheim.
Milan had a disappointing spell after their summer spending spree but the Europa League offers the seven-time European champions a chance to enjoy a successful season.
Ludogorets CEO Angel Petrichev told Tuttomercatoweb: "If Milan underestimate us they'll get a nasty shock, but I don't think that will happen. They're one of the favourites to win the whole thing, but we'll play an open game."
Borussia Dortmund, who finished third in their Champions League group behind Tottenham and Real Madrid, resume European action under new boss Peter Stoger against Serie A side Atalanta, who beat BVB 1-0 in a friendly in August.
"We've already played Atalanta in preseason," Dortmund sporting director Michael Zorc said. "They are a team with a clear defensive focus, a team who finished fourth in Italy last season to the surprise of many. This is a very attractive draw."
Italian contenders Napoli take on German club RB Leipzig, with both sides having dropped out of the Champions League.
Elsewhere, Celtic play Zenit St Petersburg, Lazio take on Romanian side FCSB and Lyon face Villarreal.
Ties to be played Feb. 15 and 22
Borussia Dortmund vs. Atalanta
Nice vs. Lokomotiv Moscow
FC Copenhagen vs. Atletico Madrid
Spartak Moscow vs. Athletic Bilbao
AEK Athens vs. Dynamo Kiev
Celtic vs. Zenit St Petersburg
Napoli vs. RB Leipzig
Red Star Belgrade vs. CSKA Moscow
Lyon vs. Villarreal
Real Sociedad vs. Red Bull Salzburg
Partizan Belgrade vs. Viktoria Plzen
FCSB vs. Lazio
Ludogorets Razgrad vs. AC Milan
Astana vs. Sporting Lisbon
Ostersunds FK vs. Arsenal
Marseille vs. Braga