The 19-year-old, who was included in Croatia's provisional 30-man squad for the ongoing World Cup, has arrived from Hajduk Split.
Speaking for the first time since his switch was finalised, Pasalic told the club's official website: "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."
The Croatia Under-21 international scored 11 goals in 36 outings for Hajduk last term.