Manchester United face Turkey's Fenerbahce and Dutch side Feyenoord in the group stage of the Europa League following the draw in Monaco on Friday.
Fellow Premier League side Southampton are in a group with Inter Milan, Sparta Prague and Israel's Hapoel Beer-Sheva.
United go into the first campaign under Jose Mourinho with one of the more difficult groups, completed by Ukraine's Zorya Luhansk.
For Fenerbahce's Dutch striker striker Robin van Persie, it means a meeting with two former clubs in Feyenoord and United.
Mourinho welcomed being drawn with Fenerbahce and Feyenoord but said he knew little about Zorya.
"There are groups in the Champions League that are very similar, so it is a good for that," Mourinho said.
"We know that it will be a difficult group, but I think that is a good thing. If you have teams without expression then even the fans may not enjoy nights at Old Trafford."
He added: "Having a team like Man United in the competition, playing matches against teams like Feyenoord and Fenerbahce - I do not have a vision about the Ukrainian team and their quality - is good for us."
German Bundesliga side Schalke can meanwhile look forward to a meeting with former Borussia Moenchengladbach coach Lucien Favre, who is now in charge of Nice, and also have former Bayern Munich centre back Dante in his squad.
Schalke also come up against Austrian side Salzburg, who went out in the Champions League play-offs to Dinamo Zagreb, and Russian outfit Krasnodar, with whom Borussia Dortmund had difficulties last season in the group stage, winning 2-1 at home and losing 1-0 away.
Schalke coach Markus Weinzierl said his side were in "a strong and exciting group" while sports director Christian Heidel said: "Nice under Lucien Favre will be tactically very, very well set up. Salzburg have high hopes and will certainly be fired up after their elimination in the Champions League."
Group A: Manchester United, Fenerbahce, Feyenoord, Zorya
Group B: Olympiakos, Apoel Nicosia, Young Boys Bern, Astana
Group C: Anderlecht, Saint-Etienne, Mainz, Gabala
Group D: Zenit St Petersburg, AZ Alkmaar, Maccabi Tel Aviv, Dundalk
Group E: Viktoria Plzen, Roma, Austria Vienna, Astra Giurgiu
Group F: Athletic Bilbao, Genk, Rapid Vienna, Sassuolo
Group G: Ajax, Standard Liege, Celta Vigo, Panathinaikos
Group H: Shakhtar Donetsk, Braga, KAA Gent, Konyaspor
Group I: Schalke, Salzburg, Krasnodar, Nice
Group J: Fiorentina, PAOK, Slovan Liberec, Qarabag
Group K: Inter Milan, Sparta Prague, Southampton, Hapoel Beer-Sheva
Group L: Villarreal, Steaua Bucharest, Zurich, Osmanispor
The group stage begins on September 15 and runs until Decemeber 8. The final will be played in Solna, Sweden on May 24