The 19-year-old, who has represented his country at Under-21 level and was named in their 30-man provisional World Cup squad, immediately joined Jose Mourinho's squad for pre-season training.
Pasalic’s move to Stamford Bridge was understood to have been agreed last season and the deal has now been confirmed.
"I am very happy because I am now a Chelsea player," he told the club's official website. "I am very impressed by the training ground and I must thank everybody at Hajduk.
"This is now a new start in my career. I am a central midfielder, my favourite player is Frank Lampard and so I am very happy to be a Chelsea player."
The German-born youngster made a promising start to senior football during the 2013/14 season, scoring 11 times in 36 appearances in all competitions and helping his side to third place in the Croatian league.
Pasalic is Chelsea's third signing of the window following the transfers of Cesc Fabregas from Barcelona and Diego Costa from Atletico Madrid, although he may be loaned out in order to gain further first team experience.
Wallace and Bertrand Traore have already made temporary moves to Vitesse Arnhem his summer, while Tomas Kalas has been loaned to Cologne and Thorgan Hazard to Borussia Monchengladbach.
Chelsea begin their 2014/15 campaign away at Burnley on Saturday August 16.