Harry Redknapp's men, in the competition after a successful foray into the Champions League last season, qualified for the play-offs automatically and will travel to Edinburgh on August 18, with the return leg at White Hart Lane a week later.
Hearts, who booked their place in the play-offs with a 4-1 win over PAKS, are now under the management of Paulo Sergio, who took the job earlier this week following the shock exit of Jim Jefferies.
It will be the first ever competitive meeting between the two sides and, in drawing each other, they avoided tricky-looking ties against the likes of Spartak Moscow and Trabzonspor.
Fulham's reward for getting past RNK Split with a comfortable 2-0 home win is a clash against Ukrainian outfit Dnipro Dnipropetrovsk.
Martin Jol's side, who have been in action in the competition since qualifying started at the end of June, will play the first leg at the Dnipro Arena, before returning to Craven Cottage.
Scottish champions Rangers will look to put their Champions League disappointment behind them against Slovenian side Maribor.
Darko Milanic's team won the Slovenian title for a ninth time last season, while Rangers were surprise casualties from the Champions League when they went out to Malmo in a two-legged play-off.
Rangers' Old Firm rivals Celtic will need to get the better of Swiss side FC Sion.
Managed by former France international Laurent Roussey, Sion lifted their 12th Swiss Cup last season, while Celtic finished runners-up to Rangers.
Stoke are also facing a trip to Switzerland after being paired with FC Thun, with the first leg at Arena Thun.
Tony Pulis' men are making their first appearance in Europe after reaching the FA Cup final last season, while Thun finished fifth and are coached by the veteran Swiss Bernard Challandes.
Carling Cup winners Birmingham, who will compete despite their relegation to the Championship, will juggle their second-tier slog with a clash against Portuguese club Nacional.
They finished sixth in the Portuguese Liga last season, while Blues, who will head to Portugal for the first leg, have endured a summer of turbulence, with manager Alex McLeish and a number of key players moving on.
Meanwhile, Irish side Shamrock Rovers were given a tough assignment after being drawn out against Partizan Belgrade, with the first game due to be played at the Tallaght Stadium.
Rovers were knocked out of the Champions League qualifying stages by FC Copenhagen on Wednesday.
Atletico Madrid will begin their campaign against Vitoria.
The 2010 winners are set to host the first leg against the Portuguese Cup runners-up in the opening leg on August 18, with the return match scheduled for seven days later.
Primera Liga rivals Athletic Bilbao will travel to Turkish side Trabzonspor for the opening match of their play-off tie, while Sevilla face a tricky tie against Hannover.
Another Bundesliga club, Schalke, will make the trip north to Finnish champions HJK Helsinki.
Braga, runners-up to Portuguese rivals Porto in last season's Europa League final, were drawn against Swiss side Young Boys, Roma take on Slovan Bratislava, with Lazio entertaining Macedonian club Rabotnicki in the opening leg.
Two Eredivisie teams were also in the draw. PSV Eindhoven will face SV Ried over two legs while Aalesund are the opponents for AZ Alkmaar.
Ligue 1 big-spenders Paris St Germain were pitted against Olympiacos Volou, the Greek club who were relegated from the Super League after being implicated in the match-fixing scandal which recently hit the country.
Volou are currently appealing the decision.
Rennes will take on Crvena Zvezda, with Sochaux looking forward to a trip to Ukraine in the opening leg of their match agains Metalist Kharkiv.
Europa League play-off round draw:
Maccabi Tel-Aviv v Panathinaikos
Atletico Madrid v Vitoria SC
Shamrock Rovers v Partizan Belgrade
Metalist Kharkiv v Sochaux
Besiktas v Alania Vladikavkaz
Rosenborg v AEK Larnaca
Vorskla Poltava v Dinamo Bucharest
Bursaspor v Anderlecht
Roma v Slovan Bratislava
Olympiakos Volou v PSG
Legia Warsaw v Spartak Moscow
Ekranas v Hapoel Tel-Aviv
PAOK v Karpaty Lviv
Trabzonspor v Athletic Bilbao
HEARTS v TOTTENHAM
NK Maribor v RANGERS
Steaua Bucharest v CSKA Sofia
Nordsjaelland v Sporting Lisbon
Dnipro Dnipropetrovsk v FULHAM
Lokomotiv Moscow v Spartak Trnava
Sion v CELTIC
Slask Wroclaw v Rapid Bucharest
Litex Lovech v Dynamo Kiev
Lazio v Rabotnicki
Nacional v BIRMINGHAM
PSV Eindhoven v SV Ried
Thun v STOKE
Aalesunds v AZ Alkmaar
Vaslui v Sparta Prague
AC Omonia v FC Salzburg
Zestafoni v Club Brugge
Hannover v Sevilla
HJK Helsinki v Schalke
Dinamo Tbilisi v AEK Athens
Rennes v Crvena Zvezda
Gaz Metan Medias v Austria Wien
Braga v Young Boys
Standard Liege v Helsingborgs
Ties to be played on August 18 and 25.