'Sky Sports News' reports that the player has passed his medical and is likely to link up with his new side in Singapore this weekend, where they are on tour preparing for the upcoming Premier League season.
The 24-year-old could barely contain his delight at the move when quizzed upon his arrival in London.
"This is the best club and Antonio Conte is one of the best coaches in the world and I'm so happy to work with Antonio," he told the gathered press.
Morata only re-signed for Real last summer after a spell with Juventus, but his 20 goals in 43 games last season helped fire Real to a La Liga and Champions League double.
The move is expected to be confirmed soon, whilst Diego Costa's situation is also expected to beocme clearer in the coming days.