British media reports said Chelsea would pay around 70 million pounds for Morata, which would shatter the club's current transfer record by eclipsing the 50 million they spent on Fernando Torres in 2011.
"Chelsea Football Club and Real Madrid have agreed terms for the transfer of Alvaro Morata to Stamford Bridge," Chelsea said in a statement.
The 24-year-old will give Chelsea manager Antonio Conte the attacking reinforcement that he has been searching for after he was reported to be frustrated by the club missing out on Belgium forward Romelu Lukaku, who joined Manchester United last week.
Chelsea were in the market for a striker as Spain's Diego Costa is expected to leave the club having not travelled on their pre-season tour to China and Singapore.
Morata, who had also been strongly linked by British media with a move to Manchester United earlier in the transfer window, helped Madrid win a second successive Champions League title last season, but spent much of the campaign as a substitute.
The former Juventus forward scored 20 goals in all competitions in 17 starts, giving him the best goals to games ratio of all Real's forwards.
It was, however, his knack of grabbing vital goals, including late winners against Sporting Lisbon, Villarreal and Athletic Bilbao, that made him a key component in Zinedine Zidane's double-winning side.
Morata was an academy graduate at Real and made his debut in 2010, but left four years later for Juventus, where he spent two seasons.
He helped Juve reach the 2015 Champions League final, scoring a decisive equaliser against Real in the semi-final, second leg. He also found the net in the 3-1 defeat by Barcelona in the final.
Yet like at Madrid, Morata failed to hold down a regular place for Juventus despite his decisive cameo appearances.
($1 = 0.7675 pounds)
(Reporting by Toby Davis; Editing by Alison Williams)
