The move is now subject to the 24-year-old agreeing personal terms and passing a medical, according to a statement released by Chelsea.
Sky sources understand the initial fee for Morata is £58m (€65.6m). If all add ons are realised, the total fee could rise to about £70m (€79.1m).
The Spain international will arrive in London on Thursday morning and is expected to sign a five-year contract once he passes his medical.
Alvaro Morata rounded off a wonderful counter-attacking move from Real Madrid to score the third and final goal against Real Sociedad
Morata reacted to the move in an interview with Spanish outlet Marca on Wednesday night, saying: "I am very happy, God willing, tomorrow I will be at Chelsea, a club that has always wanted me.
"I'm not disappointed about anything, I've won four titles here [with Real Madrid], but now I only think of putting on the Chelsea shirt.
"I want to grow up, if I didn't I wouldn't have left. I'd like to thank Zidane and wish him luck for the upcoming season.
"Thanks to all the Madridistas who supported me. I will always wish Madrid the best."
Manchester United had been in talks to sign Morata prior to the signing of Chelsea target Romelu Lukaku, but they refused to pay Real's asking price.
After missing out on Lukaku, Chelsea focused on their other targets namely Morata, Pierre-Emerick Aubameyang, Andrea Belotti and Manchester City's Sergio Aguero.
They made a decisive move for Morata on Wednesday after being told that Aguero and Borussia Dortmund's Aubameyang were not for sale.
Conte signed Morata when he was at Juventus
Torino's Belotti has been linked with a move to Serie A rivals AC Milan.
Morata was Antonio Conte's top target after Lukaku. Conte signed Morata for Juventus when he was in charge of the side in 2014, but left to manage the Italy national team shortly afterwards.
Sky sources understand the Chelsea boss still wants to sign another striker this summer, although that may just be in a back-up role.