Tottenham, among the top seeds, will face Anzhi Makhachkala plus Sheriff Tiraspol in Moldova and Tromso in Norway - 200 miles north of the Arctic circle and where the sun barely shines in winter.
Wigan will go to Rubin Kazan, Maribor of Slovenia and Zulte Waregem in Belgium while Swansea have a tough-looking group featuring Spanish side Valencia, Russian side Kuban Krasnodar and St Gallen of Switzerland.
The concern for all the clubs will be the length of the journeys and how it fits in with their domestic league matches.
Spurs at least should not have to travel to Makhachkala, home city of one-time big spenders Anzhi who have shed many of their star players in recent months in a drastic cost-cutting exercise.
Trouble with armed dissidents means that their home matches in Europe have been played in Moscow rather than at Anzhi's home stadium on the Caspian Sea.
Swansea have arguably the toughest opponents of all in Valencia, but with seven Spaniards in the squad - and manager Michael Laudrup having been in charge of La Liga side Getafe before taking over at the Liberty Stadium - they will have some inside information.
Swans general manager Alun Cowie said: "From a football point of view Valencia is the team that stood out and for our Spanish contingent they are going to be two great games.
"We have Pablo Hernandez, formerly of Valencia, and six other boys who have played at the very highest level of La Liga and we are going to need that experience.
"All three of us from the UK have Russian opponents and hopefully the fixtures will be kind to us for the Premier League matches afterwards.
"We have a great squad with virtually two players for every position, but we can't take our eye off the ball in the Premier League."
Wigan chief executive Jonathan Jackson said the Latics will enjoy their first European adventure.
He said: "Playing in Europe is about experiencing new places and going to new clubs and it's something we are really looking forward to.
"It's a group where we can certainly compete and we won't take anyone likely but we have every chance."
Full 2013-14 Europa League group stage draw:
Group A: Valencia, SWANSEA, Kuban, St Gallen
Group B: PSV, GNK Dinamo, Chornomorets Odesa, Ludogorets,
Group C: Standard Liege, FC Salzburg, Efsborg, Esbjerg
Group D: Rubin Kazan, WIGAN ATHLETIC, Maribor, Zulte Waregem
Group E: Fiorentina, FC Dnipro, Pacos Ferreira, Pandurii
Group F: Bordeaux, APOEL, Eintracht Frankfurt, Tel-Aviv
Group G: Dynamo Kyiv, Genk, Rapid Wien, Thun
Group H: Sevilla, Freiburg, Estoril, Liberec
Group I: Lyon, Real Betis, Guimaraes, Rijeka
Group J: Lazio, Trabzonspor, Legia Warsaw, Limasol
Group K: SPURS Anzhi, FC Sheriff, Tromso
Group L: AZ, Paok, Maccabi Haifa, Shakter