Mauricio Pochettino's first European match in charge will see Spurs travel to Cyprus for the first leg on August 21 with the return at White Hart Lane seven days later.
Last season Tottenham made it through the group stages of the Europa League but were eliminated by eventual runners-up Benfica in the last 16.
Hull City, who booked their place in the final qualifying draw with a 2-1 aggregate win over AS Trencin, face a tough task against Belgian side Lokeren.
Like Tottenham, Steve Bruce's side have been drawn away from home in the first leg.
Legia Warsaw, who were dumped out of the Champions League by UEFA, will meet Kazakh side FC Aktobe.
The Poles beat Celtic 6-1 on aggregate in Champions League qualifying but they were penalised for fielding an ineligible player.
Legia have already declared their intention to appeal after the result of the second leg was changed to a 3-0 defeat, which saw them eliminated on away goals.
Sarajevo v Borussia Monchengladbach
Spartak Trnava v FC Zurich
Qarabag v FC Twente
RNK Split v Torino
Neftci v FK Partizan
Apollon Limassol v Lokomotiv Moscow
Asteras Tripolis v Maccabi Tel-Aviv
Petrolul Ploeiesti v GNK Dinamo
AC Omonia v Dinamo Moscow
Ruch Chorzow v Metalist Kharkiv
Astana v Villarreal
AEL Limassol v Tottenham
HJK Helsinki v Rapid Vienna
Aktobe v Legia Warsaw
Elfsborg v Rio Ave
Young Boys v Debreceni
Dnipro v Hajduk Split
Trabzonspor v FC Rostov
Lyon v FC Astra
PSV v Shakhtyor Soligorsk
PEC Zwolle v Sparta Prague
Dinamo Minsk v Nacional
Zimbru Chisinau v PAOK
Lokeren v Hull City
Kardemir Karabukspor v Saint-Etienne
Stjarnan v Inter Milan
Panathinaikos v Midtjylland
Feyenoord v Zorya Luhansk
Grasshopper Zurich v Club Bruges
Real Sociedad v Krasnodar
Rijeka v FC Sheriff