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.