The 24-year-old striker has moved to Stamford Bridge for a reported fee of £70 million and has agreed a five-year contract, having played 43 times for the European champions last season, netting on 20 occasions.
However, he found himself surplus to requirements at the Bernabeu and has elected to join up with Antonio Conte’s side.
"I am so happy to be here," he told Chelsea's official website. "It’s an incredible emotion to be part of this big club. I am looking to work hard, score as many goals as I can and to win as many trophies as possible."
Chelsea's technical director Michael Emanelo added the club expect a great deal of him: "We believe he can make a great impact for Chelsea and look forward to seeing him in action. Alvaro has proven class at the highest level and his quality will be a huge asset to Antonio and the squad."
The striker will meet with his team-mates on their pre-season tour of Asia, as they prepare to face Arsenal in Beijing on Saturday.
Conte insisted on Friday that Morata was his first-choice target for the No.9 role, despite Chelsea's attempts to sign Romelu Lukaku before his move to Manchester United.
"I think for sure this is a good signing for us, he is a young player but has a lot of experience, he went to Juventus and Real Madrid," Conte said of him. "He has a lot of experience and I think this is a good signing for us."
Morata, who came through the Madrid youth ranks, narrowly missed playing under the Italian with Juventus, arriving at the Serie A giants for a two-season stint shortly after Conte departed for the Italy national team job, but revealed the manager’s influence played a great role in him electing to move to Stamford Bridge.
“I’m going to the team managed by the coach who has placed the most faith in me,” he said.
Willy Caballero, Antonio Rudiger and Tiemoue Bakayoko have already joined up with the Blues this summer, making Morata their fourth signing.