A statement on the club’s website read: “Chelsea Football Club and Real Madrid have agreed terms for the transfer of Alvaro Morata to Stamford Bridge.
“The move is now subject to him agreeing personal terms and passing a medical.
“Morata, 24, is a Spanish international forward, and helped Real to lift a second successive Champions League last season.”
Morata joined Real Madrid’s youth team in 2008 and was handed his senior debut aged 18 in 2010.
Real exercised a buy-back option in June 2016 to take him back to the Bernabeu.
Morata has won 20 caps for Spain, scoring nine goals, since his international debut in 2014.
Morata scored 20 goals last season after rejoining Real from Juventus.
He won La Liga and the Champions League, but the majority of his appearances were as a substitute.
Morata could replace Spain team-mate Diego Costa, who says he has been told by manager Antonio Conte that he is no longer in Chelsea’s plans.
Chelsea have been linked with Andrea Belotti, Pierre-Emerick Aubameyang, Alexis Sanchez and Sergio Aguero, but Morata is their man after Romelu Lukaku signed for Man Utd.
The sale of Morata will allow Real to step up their pursuit of Kylian Mbappe.