The Blues have agreed on a deal with Anzhi Makhachkala for the 25-year-old midfielder, who will join up with his new teammates subject to receiving a work permit.
Spurs had been the favorites to sign Willian, having agreed on a fee with Anzhi and personal terms in principle with the player, who even underwent a medical. But when Tottenham then refused to improve its salary package, Willian's representatives offered him to other clubs, and long-time admirer Chelsea made its move.
A statement on Chelsea's official website reads: "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 becomes Chelsea's third summer signing, following the arrivals of Andre Schurrle from Bayer Leverkusen and Marco van Ginkel from Vitesse Arnhem, while Wayne Rooney remains a target for manager Jose Mourinho.