Seven-times European champions AC Milan, who won an appeal against a decision to kick them out of the competition for breaking UEFA's break even rule, will meet Olympiakos and Real Betis as well as surprise package FC Dudelange from Luxemburg.
Leipzig and Salzburg were paired in Group B of Europe's second-string club competition alongside Scottish champions Celtic and Norwegian side Trondheim.
European soccer body UEFA said last year that it was satisfied that Red Bull does not have a controlling influence in both clubs, who wear their corporate colours and are closely identified with the energy drinks manufacturer.
Red Bull bought Austria Salzburg in 2005, renaming it Red Bull Salzburg, and then SSV Markranstaedt in 2009, giving it the name RB Leipzig.
Last year, it successfully argued that, following a restructuring, it no longer has a controlling stake in the Austrian club and merely sponsors it.
Milan, who last season reached the round of 16, were placed in Group F, having won an appeal at the Court of Arbitration for Sport (CAS) to allow them to take part.
UEFA argued that AC Milan did not meet a break-even requirement under its Financial Fair Play regulations, adding the club had not provided sufficient evidence of its financial stability.
But CAS said the situation had improved since U.S. hedge fund Elliott Management took control of the indebted club from Chinese businessman Li Yonghong and promised to inject 50 million euros (44.85 million pounds) to help stabilise its finances.
English Premier league side Arsenal were handed a logistical challenge when they were pitted against Ukraine's Vorskla Poltava and Azeri side Qarabag as well as Portugal's Sporting in Group E.
Chelsea will also have some travelling to do after they drew Belarus side BATE Borisov, Hungarians Vidi and Greek side PAOK in Group L.
(This version of the story changes 'BATE Boris' to 'BATE Borisov' in final paragraph.)
(Writing by Brian Homewood; Editing by Toby Davis)
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