Pasalic was due to join up with Jose Mourinho’s squad for their first pre-season training session later on Wednesday after arriving at the Premier League club’s Cobham head-quarters.
The 19-year-old is regarded as a dynamic young talent and has already featured in his country’s Under-21 team.
He was also named in Croatia’s provisional 30-man World Cup squad, but didn’t make the final cut for the tournament in Brazil and has yet to make his senior international debut.
“I am very happy because I am now a Chelsea player,” Pasalic told Chelsea’s 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 came to Chelsea’s attention after enjoying a fine first full season in senior football during 2013-14.
He scored 11 times in 36 appearances in all competitions and helped Hajduk to a third-place finish in the Croatian league.
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 Dutch club Vitesse Arnhem during the close-season, while Tomas Kalas made a temporary move to Cologne and Thorgan Hazard to Borussia Monchengladbach.
Pasalic is Chelsea’s third signing of the transfer window following the more high-profile arrivals of Spain midfielder Cesc Fabregas from Barcelona and Spain forward Diego Costa from Atletico Madrid.