Willian's transfer is subject to a work permit hearing which will take place on Wednesday this week and, provided it is granted, Chelsea will pay a fee reportedly in the region of £30million.
And, according to Sky sources, Chelsea could be on the verge of signing a second player from Anzhi, the former Barcelona superstar Eto'o.
On Friday, Chelsea boss Jose Mourinho said attacking midfielder Willian had chosen to join the Stamford Bridge club rather than Spurs.
The Brazilian had looked to be on the verge of joining Tottenham earlier this week before Chelsea entered the race.
And on Sunday morning the Blues confirmed they have struck a deal with Anzhi.
A Chelsea statement 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 got as far as completing a medical at Spurs, but Mourinho appeared to question the merit of that news being made public.
"You have to do the medical before, but the best thing to do is to do the medical in secret," said Mourinho. "If the player is fine, you can sign him. If the player is not fine you don't destroy his career.
"Every one of us managers will say we are happy with our squad, but we are always unhappy. We always want something more, something of more quality and never close the door to the possibility of adding more quality.
"Before Aston Villa I told you we have Plan B and Plan C so I was letting the door open to other possibilities.
"I want a 22 player squad so if somebody comes, somebody leaves. Do we need to sell, no we don't. Do we need to loan, probably yes because I don't like to work with big squads. I like to work with a small group of players, and I say 22 is a perfect number for our needs in different competitions."
The development with Eto'o is new, with Mourinho hoping to boost his strike options after seeing two bids for Wayne Rooney rejected by Manchester United.
Anzhi owner Suleyman Kerimov has decided to drastically reduce his spending on the football club, and Eto'o, 32, was their highest paid player.