Manchester United get intersting Europa League group
It pits United against their former striker Robin van Persie, who is now with Fenerbahce.
Southampton, the other Premier League side still in the competition, will play Inter Milan, Sparta Prague and Hapoel Beer Sheva.
League of Ireland side Dundalk have been drawn with Zenit St Petersburg, AZ Alkmaar and Maccabi Tel-Aviv.
The match dates for the group stage are 15 and 29 September, 20 October, 3 and 24 November, and 8 December.
United boss Jose Mourinho said he knew little about Ukrainian opponents Zorya, whose home ground is close to the Russian border, meaning they will play their fixtures 500 miles away in Odessa.
But welcomed being drawn with Fenerbahce and Feyenoord, who will have a reduced capacity at their De Kuip stadium due to trouble at previous games.
"We all know the competition is not the same as the Champions League but to have Manchester United playing against clubs with tradition like Fenerbahce and Feyenoord is good for us," he said.
"We know that it will be a difficult group, but I think that is a good thing. It is good for the fans and for the players because it will help motivation."
Group A: Man Utd, Fenerbahce, Feyenoord, Zorya Luhansk
Group B: Olympiacos, Apoel Nicosia, Young Boys, Astana
Group C: Anderlecht, St Etienne, Mainz, Qabala
Group D: Zenit St Petersburg, AZ Alkmaar, Maccabi Tel-Aviv, Dundalk
Group E: Plzen, Roma, Austria Vienna, FC Astra Giurgiu
Group F: Athletic Bilbao, Genk, Rapid Vienna, Sassuolo
Group G: Ajax, Standard Liege, Celta Vigo, Panathinaikos
Group H: Shakhtar Donetsk, Braga, Gent, Konyaspor
Group I: Schalke 04, FC Red Bull Salzburg, Krasnodar, Nice
Group J: Fiorentina, PAOK Salonika, Liberec, Qarabag
Group K: Inter Milan, Sparta Prague, Southampton, Hapoel Beer Sheva
Group L: Villarreal, Steaua Bucharest, FC Zurich, Osmanlispor