In a brief statement, the Blues confirmed: "Aston Villa and Chelsea can confirm that the clubs have reached an agreement for the permanent transfer of Carney Chukwuemeka.
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"The 18-year-old has been given permission to travel to London to discuss both personal terms and undergo a medical."
Sources have told ESPN that the medical is expected to take place on Wednesday with Chukwuemeka set to become the Blues' third summer signing after the arrivals of Raheem Sterling from Manchester City and Kalidou Koulibaly from Napoli.
A move abroad appeared the most likely option if Villa were pushed to sell but the size of Chelsea's offer has proved too difficult to resist: sources have told ESPN the deal comprises an initial fee in the region of £15m with add-ons taking it to a potential £20m depending on the player's progress.
Chukwuemeka won the European Under-19 Championship with England last month and is tipped for a bright future after making 12 Premier League appearances last season.