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."
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