The Real Madrid forward had been expected to join Manchester United but Jose Mourinho opted instead to sign Romelu Lukaku.
The Blues are in the market for a new striker after Antonio Conte deemed Diego Costa surplus to requirements.
The fee is thought to be in the region of £70 million.
The 24-year-old, who has hit nine goals in 20 games for the Spanish team, is currently on tour with Madrid in the US.
The deal comes a day after Blues manager Conte signed a new deal at the club.
Chelsea needed a striker. They have managed to get the best one currently on the market. Morata was reportedly always Conte’s first choice. The club, it has been widely reported, prioritised a move for Lukaku.
So, in the end, Conte got his man. But questions remain. £70 million or thereabouts represents quite the risk for a man who has no Premier League experience and was not a guaranteed starter for Real Madrid last year.
Having said that, he has proven his worth in two leagues and has all the attributes to shine in Conte’s system and the Premier League. Conte and Morata have worked together before so know what to expect of each other.