The Blues confirmed the news on Wednesday via the club's official website, with Morata set to leave Real Madrid for the second time in his career, having only returned to the Santiago Bernabeu in the summer of 2016 from Juventus.
The Telegraph's Matt Law reported the deal is worth £58 million (€65.6 million) plus add-ons and makes him Chelsea's record signing, taking the moniker from Fernando Torres, who signed from Liverpool for £50 million in 2011.
According to Fabrizio Romano of the Guardian, Morata will sign a five-year contract at Stamford Bridge:
The Spain international rejoined former club Real after the European titans exercised a €30 million (£24 million) buy-back clause to bring the player to the capital once more, per Rory O'Callaghan of MailOnline.
BBC Sport's Simon Stone commented on Morata's move being of significantly lower cost than Romelu Lukaku's £75 million move to Manchester United, pertinent given the Red Devils were previously interested in Real's man:
Morata, 24, netted 20 times in 43 appearances for Real last season but was used largely as back-up to Karim Benzema and started in only 19 of those appearances.
What's more, he played the full 90 minutes on only six occasions across all competitions, so while Real won a UEFA Champions League and La Liga double, Morata will have surely been left feeling somewhat hollow in the achievement.
Chelsea manager Antonio Conte has shown faith in the young Spaniard after they came close to working with one another at Juventus, although the tactician had departed for Italy's helm by the time Morata arrived.
In essence, this will be Morata's first post as a senior starter considering he was forced to play off the bench a lot during his two seasons at Juventus and rarely commanded a start in Real's more essential fixtures.
The striker has shown glimpses of his prolific potential and has climbed Spain's youth ranks for years as a prospect, but Conte finally looks ready to unleash Morata upon the Premier League and beyond.