This news came in late Saturday night, as reported by Fabrizio Romano and many other reliable sources.
The fee is £45million plus £10million in potential add-ons.
Chelsea had earlier agreed personal terms with the English winger days ago.
The duration of the contract runs until 2027 with an option for a further year.
Sources close to the deal emphasized that the deal was never in doubt and all that remains now is for Chelsea to conduct medicals for the player.
The Club World Champions hope to conduct a successful medical for the winger in time for him to meet up with his new teammates on their U.S.A tour.