"The move is now subject to him agreeing personal terms and passing a medical", Chelsea said in a statement. The Spain worldwide must now agree personal terms and pass a medical to complete the transfer.
Chelsea have reportedly agreed a £70.6m fee with Real for Morata.
The London club says it has agreed terms with Madrid to sign the 24-year-old striker.
Chelsea have thus far signed German defender Antonio Rudiger from Roma, goalkeeper Willy Caballero fro Manchester City and midfielder Timeoue Bakayoko from Monaco.
Morata enjoyed a rather productive 2016/17 campaign for Madrid despite not being considered a regular under Zinedine Zidane.
Morata has always been a favourite with Antonio Conte and the Chelsea manager agreed his new two-year contract in the knowledge the club would push to deliver quality additions to his title-winning squad.
He scored 15 goals in 26 appearances in La Liga last season, the most prolific spell of his career.
That left the way clear for Chelsea to step up their bid for the Spanish star, who played under Blues boss Antonio Conte at Juventus.
Chelsea are unlikely to sanction a move until they bring in a replacement, and they could yet face competition from AC Milan for Morata.