Stoke face the Croatian giants in the first leg of the third qualifying round tie at the Britannia Stadium hoping to give themselves a good platform heading into next Thursday's away match.
Pulis said: "It's exciting times. It's part of what has been a fantastic five years at the football club. To have the opportunity of playing a European game at the Britannia against such a famous side as Split is first class. We're all looking forward to it.
"We think they're a good side. We've watched tapes of them from the back end of last season and pre-season and we've been out and watched them. We know a little bit about them.
"But it's a home game for us and irrespective of what they do or they don't do, the priority is that we're prepared, we're right and give it the best shot we possibly can.
"Today and tomorrow will all be about us, it won't be about Split. Out of the teams we could have been drawn against, this is as hard a game as we could have had, but it's great and it's really caught the imagination of the local public.
"The place will be rocking. They tell me the atmosphere in Split is fantastic - well let's see what they think of our atmosphere."
The Potters qualified for Europe for the first time since losing to Ajax in the 1974/75 UEFA Cup first round by reaching last season's FA Cup final, which they lost 1-0 to Manchester City.
Their only previous European experience came two seasons before that when they were beaten over two legs by Kaiserslautern, so seeing off Hajduk to reach the play-off stage would represent a significant first for the club.
Pulis admitted the early start to the season has presented him with a few headaches, but he is certainly not complaining.
He said: "The preparation has been different, we've had to move things around and work the players a lot harder than we normally would in the first two weeks of pre-season, but the opportunity of playing in Europe is fantastic and we want to give it our best.
"We want to win the game, that's how important it is to us. It's early for us and we have other objectives but we want to win the game, we're desperate to win the game."
Progressing to the group stage would challenge Pulis' squad further, but he added: "You have to cope with things. We have to remember we're very, very privileged. Playing one extra game a week, we'll cope with that."
Stoke have been quiet in the transfer market, with only Jonathan Woodgate, who has joined on a pay-as-you-play deal following his departure from Tottenham, arriving at the Britannia Stadium.
The former England defender played only four games over the past two seasons because of injury problems but lasted an hour of a pre-season clash with Aldershot at the weekend and could make his competitive debut against Split.
Pulis refused to name any of his remaining transfer targets, but said: "We're desperately keen to get quite a few more in but we'll do it on our budget.
"We've been linked with everybody but we'll try to do our business with other football clubs and you hope things will drop for you."
Pulis also categorically denied the club would consider selling captain Ryan Shawcross, adding: "We won't sell our best young players. We don't have to.
"We're a club that is solvent. We think this is a good football club and a club that can push on. Fingers crossed more young players will want to join us."
Pulis will select a full-strength side on Thursday providing Matthew Etherington and Jermaine Pennant recover from knocks and Jon Walters a virus.