There remains question marks over the Turkish side's participation in the competition, while Celtic will face Shakhtar Karagandy of Kazakhstan after overcoming Elfsborg
The Turkish side will host the first leg, which is to be played on August 20, before the return leg the following week, but their participation in the competition remains in doubt "pending disciplinary and CAS proceedings".
Fenerbahce previously looked set to miss out on European football due to a 24-month continental ban for their part in the Turkish match-fixing and corruption scandal.
A number of ex-Premier League players currently make up the Fenerbahce squad, such as former Liverpool striker Dirk Kuyt and ex-Chelsea man Raul Meireles.The ties come three days after Arsenal's opening Premier League fixture of the season against Aston Villa.
Meanwhile, Celtic will travel to Kazakhstan to face Shakhtar Karagandy, also playing away in the first leg, after overcoming Elfsborg 1-0 on aggregate in the third qualifying round.
Draw in full:
Dinamo Zagreb v Austria Vienna
Ludogorets v Basle
Plzen v Maribor
Shakhtar Karagandy v Celtic
Steaua Bucuresti v Legia Warsaw
Lyon v Real Sociedad
Schalke v Metalist Kharkiv
Pacos Ferreira v Zenit St Petersburg
PSV v AC Milan
Fenerbahce v Arsenal