Tottenham will begin their Europa League campaign against Dinamo Tbilisi in the play-off round.
Andre Villas-Boas' side, who reached the quarter-finals last season, were paired with the Georgians in the draw at UEFA's headquarters in Nyon.
Capital One Cup winners Swansea, who reached this stage with a 4-0 aggregate win over Swedish club Malmo in qualifying, will face Romanian side Petrolul Ploiesti.
Spurs made a sustained challenge in the competition eventually won by Chelsea last season, bowing out only penalties to Basle at the last-eight stage.
They had high hopes of qualifiying for the Champions League this time but finished fifth in the Barclays Premier League, a point behind fourth-placed Arsenal, to find themselves in Europe's second-tier event again.
Swansea are returning to European competition for the first time since 1991 and have already shown appetite with their destruction of Malmo. All four of their goals came in the first leg of the third-round qualifier at the Liberty Stadium.
Spurs were drawn away for the first leg of their tie against the Georgian double winners with Swansea initially hosting Ploiesti, although that could be subject to change.
The first legs are due to take place on August 22 with the return a week later.
Swansea and Spurs open their Premier League campaigns against Manchester United and Crystal Palace respectively on the weekend of August 17-18 and face each other the following week.
Victories for both sides in their Europa play-offs would earn them a place in the group stage alongside FA Cup winners Wigan.
Sevilla will face Polish side Slask Wroclaw in the play-off round as they attempt to make another push for silverware.
UEFA Cup winners in 2006 and 2007, Sevilla have since had Champions League experience, however they could only finish ninth in the Primera Division last term.
That proved enough to earn a place in the Europa League qualifying stages, due to Malaga and Rayo Vallecano being excluded from European competition and Copa del Rey winners Atletico Madrid earning a Champions League place.
Unai Emery's team saw off Mladost Podgorica 9-1 on aggregate in the third qualifying round and will take on a side that finished third in the Ekstraklasa last season, with Slask Wroclaw at home in the first leg on August 22 and Sevilla staging the return seven days later.
Dutch giants Feyenoord tackle Russians Kuban Krasnodar, while Serie A side Udinese play Czech team Slovan Liberec.
Other ties see Real Betis heading to the Czech Republic first to encounter FK Jablonec, while Stuttgart will also be on their travels on August 20 when they play Croatian side HNK Rijeka.
Eintracht Frankfurt will go up against Azerbaijani side Qarabag, while French outfit St Etienne play Denmark's Esbjerg.