The 19-year-old midfielder only joined Chelsea earlier this month from Hajduk Split but has immediately been sent out on loan, with Chelsea manager Jose Mourinho keen for Pasalic to gain first-team experience.
Pasalic, who scored 11 goals in 32 appearances for Split last season, was named in Croatia’s provisional 30-man World Cup squad but did not make it to Brazil.
After Elche’s sporting director flew to London for talks, the club that narrowly avoided relegation from La Liga last season announced that Pasalic had passed his medical and begun training with his new team-mates.
Speaking at his official presentation, Pasalic said: "I wanted to play in La Liga and my coach (Jose) Mourinho thought the best thing for me was to come to Spain to play against big teams.
"I'm grateful for this opportunity with Elche. I've come here because I believe I can be an important player and help the club have a good season."