Steve Bruce's Tigers will get their first ever taste of continental football when they take on a team from either Slovakia or Serbia in the third qualifying round
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.