Pasalic, 19, joins for an undisclosed fee from Hajduk Split, where he scored 11 goals in 36 appearances as they finished third in their domestic league last season.
“I am a central midfielder, my favourite player is Frank Lampard, and so I am very happy to be a Chelsea player,” said the German-born prospect, who was named in Croatia’s provisional World Cup squad.
Pasalic is Chelsea’s third signing of the summer, following £32m Atletico Madrid striker Diego Costa and £27m Barcelona midfielder Cesc Fabregas.
The Blues are also seeking a left-back, having allowed Ashley Cole to leave on a free transfer.
Lampard’s contract also expired at the end of last season and the 36-year-old, Chelsea’s all-time top scorer, is weighing up offers from Australia and the United States.