Manchester United will play Club Brugge in the Europa League’s round of 32 and Arsenal have been drawn against Olympiacos.
United finished top of Group L and will take on Belgian side Brugge, who failed to qualify for the Champions League knockout phase.
Arsenal’s Greek opponents Olympiacos also dropped into the Europa League after finishing third in their Champions League group behind Tottenham.
Wolves have been drawn to play Spanish club Espanyol, Scottish champions Celtic face FC Copenhagen and Rangers take on Portuguese side Braga.
Arsenal finished top of Group F and club secretary David Miles said the last-32 tie was a top priority for the managerless London club.
Miles told BT Sport: “We have played Olympiacos quite a few times.
“We have good friendships. They are one of the best teams in Greece. We know they are strong. We take no-one for granted and will do our homework.
“This could be a route into the Champions League for next year, so I think this will be a priority.”
The Gunners turned in another disappointing display in their 3-0 home Premier League defeat to Manchester City on Sunday, but Olympiacos coach Pedro Martins will pay little attention to his opponents’ domestic troubles.
“It’s a big challenge for us to play against Arsenal, last year’s UEFA Europa League finalists,” Martins told UEFA’s official website.
“They may not have started well in the Premier League this season, but they have great players, are dangerous and deserve our respect.”
The first legs of the Europa League round of 32 will take place on February 20 and the second legs on February 27.
Other notable ties include Getafe against Ajax, Roma versus Gent and Inter Milan against Ludogorets.
Bayer Leverkusen face Porto and fellow Bundesliga side Eintracht Frankfurt will play Salzburg, who finished behind Liverpool and Napoli in their Champions League group.
Ajax, Roma and Inter Milan also failed to qualify for the Champions League knockout phase.
Another eye-catching tie sees Shakhtar Donetsk, who finished third in Manchester City’s Champions League group, take on Benfica.