The west London outfit said on Wednesday they had agreed a deal to sign the 24-year-old who has now passed his medical and will join the squad on their pre-season tour of Asia.
"I'm so happy to be here. It’s an incredible emotion to be part of this big club. I'm looking to work hard, score as many goals as I can and to win as many trophies as possible," Morata said on the club website (www.chelseafc.com).
British media reports said Chelsea would pay about 70 million pounds ($90.92 million) for Morata, which would shatter their transfer record of 50 million for Fernando Torres in 2011.
Chelsea were looking for a striker because their Brazilian-born Spain international Diego Costa is set to leave the club having not travelled on their tour to China and Singapore.
"Alvaro has proven class at the highest level and his quality will be a huge asset to (manager) Antonio (Conte) and the squad," said Chelsea technical director Michael Emenalo.
Morata came through the youth ranks at Real and made his debut in 2010, but left four years later for Juventus.
He helped the Italians reach the 2015 Champions League final, scoring a decisive equaliser against Real in the semis.
Real exercised a buy-back option last year and Morata helped them win the Spanish title and a second straight Champions League last season but usually found himself on the bench.
He scored 20 goals in all competitions in just 17 starts, giving him the best goals to games ratio of all Real's strikers.
Morata has also scored nine goals in 20 appearances for Spain, including three at last year’s European Championship.
($1 = 0.7699 pounds)
(Writing by Ken Ferris; Editing by Pritha Sarkar)
