Liverpool have been drawn against Rubin Kazan, Bordeaux and Sion in Group B of the Europa League.
Tottenham have been handed a daunting group in the Europa League including a long haul trip to Azerbaijan.
Spurs were drawn in Group J with Monaco, Anderlecht and FK Qarabag, who play matches in Azerbaijan's capital Baku.
Celtic have the prospect of facing Robin van Persie and Nani's new side Fenerbahce plus Ajax and Molde from Norway in Group A.
The financial rewards of the Europa League have been increased by UEFA this season - and there is the carrot of the winners qualifying automatically for next season's Champions League.
Celtic's head of operations Ronnie Hawthorn said: "I think the stature of the Europa League is growing and the competition is getting more and more difficult. It's good for fans who wants to watch European competition but it is a tough competition these days.
"There is an increase in Europa funding - something like a 63 per cent increase which is quite significant - and that is an important step forward for the competition, and there are lots of good groups here including our own.
"To see players like Van Persie will be so attractive for the fans and how they are coped with in terms of our own team. That can make the match all the more interesting.
"It is also an important step for the competition that the Europa winners now access the Champions League - as Sevilla have shown last season."
Tottenham's group includes meetings with Anderlecht, the Belgian side they beat on penalties in the 1984 UEFA Cup final, the last time Spurs triumphed in a European competition. Some 13 years after the final, UEFA banned Anderlecht from Europe for a year after it emerged they had bribed the referee in the semi-final against Nottingham Forest.