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 Basel 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.