Steve Bruce's side qualified for Europe's second-tier club competition by virtue of reaching the final of the FA Cup last term and will enter at the third qualifying round.
Trencin hold a 4-0 first-leg advantage over Vojvodina ahead of Thursday's trip to Serbia and will likely host Hull for the first leg on July 31.
Elsewhere in the draw, last season's Europa League quarter-finalists Lyon will take on Mlada Boleslav or Siroki Brijeg.
Hubert Fournier's side finished fifth in Ligue 1 last term and saw their European campaign ended by Serie A champions Juventus.
The French side beat Viktoria Plzen on their way to the last eight, with the Czech side drawn against either Romanian outfit Petrolul Ploiesti or Flamurtari of Albania.
Former European champions PSV get their Europa League adventure up and running against Botev Plovdiv or St Polten while Spanish club Real Sociedad await the winners of Groningen versus Aberdeen.
Draw in full:
Kardemir Karabukspor v Rosenborg or Sligo Rovers
Trencin or Vojvodina v Hull City AFC
Sarajevo or Haugesund v Atromitos
Ruch Chorzow or Vaduz v Kairat Almaty or Esbjerg
Chornomorets Odesa v RNK Split or Hapoel Beer Sheva
Buducnost Podgorica or Omonia v Metalurg Skopje or FK Zeljeznicar
Real Sociedad v Aberdeen or Groningen
Dinamo Moscow v Hapoel Kiryat Shmona
Luzern or St Johnstone v Zestafoni or Spartak Trnava
Torino v Brommapojkarna or Crusaders
Astana or Hapoel Tel-Aviv v Linfield or AIK Solna
Young Boys v Ermis Aradippou
Mainz v RoPS Rovaniemi or Asteras Tripolis
PSV v Botev Plovdiv or St Polten
Zulte Waregem or Zawisza Bydgoszcz v Derry City or Shakhtyor Soligorsk
Elfsborg or Inter Baki v Neman Grodno or FH
Litex Lovech or Diosgyori VTK v JK Sillamae Kalev or Krasnodar
Motherwell or Stjarnan v JK Nomme Kalju or KKS Lech Poznan
FK Cukaricki or SV Grodig v CSKA Sofia or Zimbru Chisinau
Petrolul Ploiesti or Flamurtari v Viktoria Plzen
Mlada Boleslav or Siroki Brijeg v Lyon
Laci or FC Zorya Luhansk v Molde or ND Gorica
Astra v MFK Kosice or Slovan Liberec
Vikingur or Tromso v Rijeka or Ferencvarosi
Dinamo Minsk or Myllykosken Pallo-47 v Cluj or Jagodina
Neftci PFK or Koper v Bursaspor or Chikhura Sachkhere
Gyori ETO or IFK Gothenburg v Rio Ave
Club Brugge v Brondby
Atlantas or Shakhter Karagandy v Dundalk or Hajduk Split
