The 19-year-old, who was named in Croatia's provisional 30-man World Cup squad, will join up with Jose Mourinho's squad for its first pre-season training session on Wednesday afternoon.
"I am very happy because I am now a Chelsea player," Pasalic told Chelsea's official club 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."
Pasalic completed his first full campaign in senior football last season, scoring 11 times in 36 appearances in all competitions and helping Hajduk finish third in the Prva HNL, Croatia's top tier.
The German-born teenager made his first-team debut towards the end of the 2013/13 season and has represented Croatia at Under-21 level.
Pasalic may follow in the footsteps of a number of Chelsea's young prospects by being sent out on loan to gain more first-team experience.
The Blues have already loaned Wallace and Bertrand Traore to Vitesse this summer as well as Tomas Kalas to Cologne and Thorgan Hazard to Borussia Monchengladbach.
Pasalic is Chelsea's third signing of the window following the transfers of Cesc Fabregas from Barcelona and Diego Costa from Atletico Madrid.