The news which has been a made official via the club's official website this evening is subject to the Spain worldwide, who helped Los Blancos win La Liga as well as the Champions League last season, successfully passing a medical.
Morata left the practice session held by Real Madrid at the University of California-Los Angeles (UCLA) campus.
After plenty of anticipation, it appears that Chelsea FC will send a hefty transfer fee to Real Madrid in order to bring in star striker Alvaro Morata from the Spanish side.
The fee is thought to be in the region of £70 million.
The 24-year-old joined the 20-time top-flight champions from Everton for an initial £75m.
The 24-year-old becomes the Blues' fourth signing of the summer after Willy Caballero, Antonio Rudiger and Tiemoue Bakayoko, whilst it takes the club's spending close to £150m.
With Diego Costa seemingly on his way out of the club, Chelsea were forced to act quickly in their attempts to sign a striker. Overall he has netted 25 goals in 63 La Liga appearances for Real Madrid over the years with most of his appearances coming off the bench.
Chelsea may finally be about to get some good news this summer, after Ladbrokes suspended betting on Alvaro Morata's future.