Tottenham and Swansea both face trips to Eastern Europe in their quest to reach the Europa League group stages.
Swansea, who overcame Malmo 4-0 on aggregate in the third qualifying round on Thursday night, have been drawn against Romania's Petrolul Ploiesti in the play-off round, with the first leg at home.
Petrolul, who last won the Romanian championship almost 50 years ago, qualified for the Europa League by winning last season's domestic cup.
Dinamo Tbilisi stand between Tottenham and a group stage berth, with the first leg in Georgia.
Tottenham have met met Tbilisi once before, in the 1973-74 Uefa Cup, drawing 1-1 away and winning 5-1 at White Hart Lane. They went on to lose to Feyenoord in the final over two legs.
FA Cup winners Wigan qualify automatically for the group stages, while Scotland's three hopefuls - St Johnstone, Hibernian and Motherwell - all fell in the qualifying round stages.
The play-off ties will be played on 22/29 August.
Spurs made a sustained challenge in the competition eventually won by Chelsea last season, bowing out only penalties to Basel at the last-eight stage.
They had high hopes of qualifying for the Champions League this time but finished fifth in the 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.
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.
Europa League draw
FC Kuban Krasnodar v Feyenoord
SV Zulte Waregem v APOEL FC
SK Rapid Wien v FC Dila Gori
Tromso IL v Besiktas JK
CS Pandurii Lignitul Targu Jiu v SC Braga
Apollon Limassol FC v OGC Nice
FC Aktobe v FC Dynamo Kyiv
Swansea City v FC Petrolul Ploiesti
Atromitos FC v AZ Alkmaar
FH Hafnarfjordur v KRC Genk
IF Elfsborg v FC Nordsjaelland
WKS Slask Wroclaw v Sevilla
FC Salzburg v VMFD Zalgiris
arabag FK v Eintracht Frankfurt
FC Minsk v R. Standard de Liege
FK Jablonec v Real Betis
HNK Rijeka v VfB Stuttgart
FC Chornomorets Odesa v KS Skenderbeu
Maccabi Tel-Aviv FC v PAOK FC
FC St Gallen v FC Spartak Moskva
Molde FK v Rubin Kazan
FK Vojvodina v FC Sheriff
Trabzonspor AS v FK Kukesi
Esbjerg fB v AS Saint-Etienne
Grasshopper Club Zurich v Fiorentina
Maccabi Haifa FC v FC Astra
Udinese v FC Slovan Liberec
FC Dinamo Tbilisi v Tottenham Hotspur
Estoril Praia v FC Pasching
JK Nomme Kalju v FC Dnipro Dnipropetrovsk
FK Partizan v FC Thun
Matches will be played on August 22 and 29