The playmaker still need a work permit to complete the deal.
The Blues have not revealed the amount they will pay the financially-stricken Russian club, but the deal is understood to be worth around £32 million.
Tottenham Hotspur had looked set to sign the Brazilian earlier this week, having agreed a fee worth around £30 million
with Anzhi and personal terms with the player – who underwent a medical.
But Chelsea hijacked the move at the eleventh hour and, last-minute complications notwithstanding, now look set to complete the signing of the 25-year-old Brazilian playmaker.
A statement on http://www.chelseafc.com read: “Chelsea Football Club can confirm an agreement has been reached with both Willian and his club Anzhi Makhachkala for the transfer of the Brazilian player.“The transfer is subject to a work permit hearing on Wednesday.
Willian had been targeted by top English clubs including Liverpool and is now expected to bolster an already star-studded Chelsea forward.
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