Shakhtar, in Monaco for Friday's European Super Cup match against European champions Barcelona, should advance from their group in their bid to retain the cup they won so impressively last season.
Those competing in the group stages will play each other home and away as Europe's second tier competition now reflects more closely that of the Champions League.
The old UEFA Cup system of five team groups from which three teams qualified has been replaced by a format which will see the top two teams in each group qualifying for the knockout round of 32, joined by he eight teams dropping down after finishing third in their Champions League groups.
Former European champions Hamburg SV, who will host the final next May, were drawn to play another former European champion Celtic plus Hapoel Tel Aviv and Rapid Vienna, who qualified for the group stages by knocking out Aston Villa of the Premier League on away goals in their qualifying playoff on Thursday.
Celtic's Head of Operations Ronnnie Hawthorn told Reuters after the draw: "It is always good to win a competition, but it would be particularly good to become the first winners of the Europa League, especially as we were also the first British club to win the European Cup in 1967."
Besides Hamburg and Celtic, there are many other former European champions and previous UEFA Cup winners taking part, including Ajax Amsterdam who were drawn to play Anderlecht, Dinamo Zagreb and Timisoara of Romania.
Benfica, European champions in 1961 and 1962, face former European Cup Winners Cup winners Everton, AEK Athens and BATE Borisov in the group while PSV Eindhoven, European champions in 1988, face FC Copenhagen, Sparta Prague and CFR Cluj.
There is an eye-catching pairing of Panathinaikos of Greece and Galatasaray of Turkey, UEFA Cup winners in 2000, who are in the same group as Sturm Graz of Austria and Dinamo Bucharest, ordered by UEFA to play two home matches behind closed doors following crowd trouble in the qualifying rounds.
Werder Bremen, beaten by Shakhtar in last season's UEFA Cup final, face Austria Vienna, Athletic Bilbao and Nacional of Portugal as they bid to go one better this season.
The Europa League will also be notable this season for the introduction of UEFA's experimental five-man refereeing teams with an additional assistant referee placed beside each goal to assist the match referee on incidents in and around the penalty area.
The competition gets underway on Sept.17 with the final in Hamburg on May 12 next year.
