Swansea will also come up against Russian club Kuban Krasnodar, who beat Feyenoord in the play-offs and whose squad includes France striker Djibril Cisse, as well as Swiss side St Gallen in Group A.
But it is the meeting with Valencia that will most excite the fans of the Welsh club, who won the English League Cup last season.
Michael Laudrup has close links to Spain, having played for Barcelona and Real Madrid and later coached both Getafe and Mallorca. He famously took Getafe to the quarter-finals of the UEFA Cup in 2008, only losing to Bayern Munich in extra-time.
And he has injected a heavy Spanish influence into his Swansea side, with ex-Valencia winger Pablo Hernandez one of seven Spaniards in the squad.
Meanwhile, Tottenham Hotspur were handed a kind-looking draw, the Londoners finding themselves in Group K along with Sheriff Tiraspol of Moldova, Tromso of Norway and Anzhi Makhachkala of Russia.
Anzhi would have been a fearsome proposition had their billionaire owner Suleiman Kerimov not recently decided to drastically reduce the budget, leading to a mass exodus of players, most notably Samuel Eto’o, who has gone to Chelsea.
Tromso, meanwhile, lost in the play-offs to Besiktas but replaced the Turkish side, who have been banned from European competition for their role in a domestic match-fixing scandal in 2011.
FA Cup holders Wigan Athletic will also face Russian opposition in the shape of Rubin Kazan, with Slovenian champions Maribor and Zulte Waregem of Belgium completing the Group D line-up.
Elsewhere, highly-fancied Italian side Fiorentina were drawn in Group E with wealthy Ukrainian club Dnipro, who are coached by Juande Ramos, the Spaniard who led Sevilla to successive UEFA Cup triumphs in 2006 and 2007
Other notable match-ups include French Cup holders Bordeaux facing Eintracht Frankfurt of Germany in Group F, a section that also includes APOEL. The Cypriots were lucky play-off round losers, being drawn out of a hat to replace Fenerbahce after they, too, were banned from Europe for their role in the Turkish match-fixing scandal.
In Group H, Sevilla will face Freiburg, the Germans who surprisingly finished fifth in last season’s Bundesliga, while after losing to Real Sociedad in the Champions League play-offs, French club Lyon were drawn against Spanish opposition once again, facing Betis in Group I.
Dutch club AZ Alkmaar completed the line-up on Friday, being drawn in Group L after beating Atromitos of Greece on away goals.
They played out the remainder of their second leg the morning after a fire at the AZ Stadion had led to its abandonment after 59 minutes.
The first group games will be played on September 20.