Arsenal will face trips to Belarus, Germany and Serbia in the Europa League, while a new-look AC Milan have been handed a favourable-looking draw.
Arsene Wenger's Arsenal missed out on Champions League qualification after finishing fifth in the Premier League last term.
The Gunners are consequently playing in Europe's second-tier competition for the first time since 2000, where they reached the final of the UEFA Cup, and were drawn in Group H with BATE Borisov, Cologne and Red Star Belgrade in Friday's draw in Monaco.
Vincenzo Montella's Milan are back in European competition for the first time since the 2013-14 season and the Rossoneri will fancy their chances of progressing from a Group D also including Austria Vienna, Rijeka and AEK Athens.
Group E promises some nice trips for Everton fans following their victory over Hajduk Split in the play-off round. The Toffees were drawn out with Lyon - where the final will be held - Atalanta and Apollon Limassol.
Nice were denied a Champions League place by Napoli in the play-off round and they will face another Italian test in the Europa League having been drawn with Lazio.
The two sides are joined in Group K by Zulte Waregem and Vitesse from Belgium and Netherlands respectively, while Rosenborg - conquerors of last season's beaten finalists Ajax - were rewarded with clashes against Zenit, Vardar and Real Sociedad in Group L.
The group stages of the Europa League will begin on September 14 and the tournament victors will earn a place in the Champions League.