Defending UEFA Champions League champions Bayern Munich will meet Manchester City, CSKA Moscow and Viktoria Plzen in the group stages, after the draw took place on Thursday night.
Spanish giants Real Madrid and Barcelona face some interesting battles in the group stages.
AC Milan are making it a habit of meeting Barca in the Champions League as the Spanish and Italian giants were paired together in Group H. Ajax will also be thrown into the mix, while Celtic complete the group.
Madrid, the nine-time champions, drew Italian champions Juventus as well as Turkish side Galatasaray and FC Copenhagen.
Manchester United manager David Moyes will be fairly pleased with his draw, though a line-up of Shakhtar Donetsk, Bayer Leverkusen and Real Sociedad could be tricky.
Arsenal face last year's runners-up Borussia Dortmund, along with French side Marseille and Italian side Napoli in what seems to be a difficult group on paper.
Chelsea manager Jose Mourinho will feel slightly confident after the Blues were drawn to meet German side Schalke, FC Basel and Steaua Bucuresti.
Big-spending French side Paris Saint-Germain were paired with Portuguese side Benfica, Olympiakos and Anderlecht.
Porto face stiff competition from Spaniards Atletico Madrid, Zenit St Petersburg and Austria Vienna.
Group A: Manchester United, Shakhtar Donetsk, Bayer Leverkusen, Real Sociedad
Group B: Real Madrid, Juventus, Galatasaray FC Copenhagen
Group C: Benfica, Paris Saint-Germain, Olympiakos, Anderlecht
Group D: Bayern Munich, CSKA Moscow, Man City, Viktoria Plzen
Group E: Chelsea, Schalke, FC Basel, Steaua Bucuresti
Group F: Arsenal, Marseille, Borussia Dortmund, Napoli
Group G: Porto, Atletico Madrid, Zenit St Petersburg, Austria Vienna
Group H: Barcelona, AC Milan, Ajax, Celtic