The Premier League club have waited a long time for their maiden continental adventure and they will be expected to mark their first competitive fixture outside the UK with a victory.
Hull played in their first major final when they were beaten by Arsenal in the FA Cup showpiece at Wembley in May and qualified for the Europa League as a result.
Boss Steve Bruce admitted competing in Europe can be a "huge complication" due to the number of games they will play if they qualify for the group stage, but embraced the prospect of becoming the first manager to lead Hull into a European fixture.
The 2013-14 campaign was one to savour for Hull fans, as they preserved their Premier League status in their first season back in the top flight as well as enjoying trips to Wembley for the semi-final and final for the FA Cup.
And they will be determined to start the new season on a high note against a Trencin side that were runners-up in the Slovakian Super Liga last season and have won their opening two league games of the new campaign.
As well as being a landmark game for Hull, Thursday's fixture will also be Bruce's 100th at the helm and the former Sunderland boss is no doubt his side will be prepared despite a disappointing friendly display against League One Barnsley at the weekend.
He said: "We'll be as ready as what we will be.
"It was a pre-season friendly where nobody could tackle a fish supper, never mind a football, so it was a normal pre-season affair. But make no mistake, we will be better on Thursday.
"When the proper ball comes out for a cup competition, then all of a sudden there's a different mentality."
Trencin withstood a second-leg fightback from Serbian club Vojvodina in the second qualifying round to prolong their participation in the Europa League.
Moses Daddy-Ajala Simon scored a hat-trick as Ivan Vrabec's side coasted to a 4-0 victory in the first leg, but they then suffered a 3-0 defeat in the return fixture as Vojvodina gave them a real scare.
The likes of Robert Snodgrass, Tom Ince, Harry Maguire and Andy Robertson could make their competitive Hull debuts in Slovakia, with Bruce having been busy in the transfer market.
Bruce will monitor the fitness of Alex Bruce (Achilles), Curtis Davies (hamstring), David Meyler (knee) and Allan McGregor (knee).