The Croatia under-21 international midfielder was named in Niko Kovac's initial 30-man squad for the World Cup, but he failed to make the final cut for the group which travelled to Brazil.
After completing his move, the 19-year-old revealed Stamford Bridge legend Frank Lampard is his favourite player.
I am very happy because I am now a Chelsea player.
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.
Lampard left Chelsea at the end of the last Premier League season after 13 trophy-laden years with the club, but Blues fans will be delighted to hear that the Croatian youngster already has such a strong interest in the club and particularly its record goalscorer.
Pasalic scored 11 times for Hajduk Split in 30 appearances in the Croatian league last season.
According to Bleacher Report's Sasa Ibrulj, the young midfielder will be one of the players coming through the ranks to feature for Croatia in the Euro 2016 qualifying campaign.
Pasalic is a product of the Hajduk Split youth academy. After joining the club in 2006, he made his first-team debut as a substitute against HNK Cibalia in April 2013.
His development since then has convinced Chelsea manager Jose Mourinho to snap him up for the London club.
Pasalic has now joined up with the rest of the first-team squad at Chelsea's training base in Cobham, Surrey, where he will be working alongside John Terry, Nemanja Matic and other members of the squad before those Blues players involved in the World Cup return.