The France international has moved from Bolton Wanderers after agreeing terms on a four-and-a-half-year contract.
It had been reported that Chelsea were cooling on the idea of signing Anelka after the protracted transfer reached an impasse regarding the size of the fee.
The Stamford Bridge club initially bid £11m for the 28-year-old, but Bolton were determined to hold out for their original valuation of £15m.
After lengthy talks Chelsea eventually conceded to Bolton's request and have paid the full amount.
Today's announcement means Anelka has signed in time to play against Tottenham at home on Saturday.
Chelsea have been keen to sign Anelka for some time now to compensate for the departure of Ivory Coast internationals Didier Drogba and Salomon Kalou to the African Cup of Nations.
Avram Grant will be without leading scorer Drogba and Kalou for about a month, and with Andriy Shevchenko injured and Claudio Pizarro in unconvincing form, the club have been left short in attack as they challenge for the Premier League and Champions League.
Anelka, who signed a new four-year contract at Bolton in August, has scored 11 goals this season.
The former Paris Saint-Germain, Arsenal, Real Madrid, Liverpool, Manchester City and Fenerbahce forward cost Bolton £8m back in 2006.
His move to Chelsea makes him the most expensive player in the world, based on cumulative transfers.
Juan Sebastien Veron previously held the record, but Anelka's latest big-money move means he has now cost clubs a staggering £84.8m throughout his career.
The Frenchman was previously third on the all-time transfer fee list, but now moves above Veron and Hernan Crespo as the most valuable player on the planet.
It had been reported that Chelsea were cooling on the idea of signing Anelka after the protracted transfer reached an impasse regarding the size of the fee.
The Stamford Bridge club initially bid £11m for the 28-year-old, but Bolton were determined to hold out for their original valuation of £15m.
After lengthy talks Chelsea eventually conceded to Bolton's request and have paid the full amount.
Today's announcement means Anelka has signed in time to play against Tottenham at home on Saturday.
Chelsea have been keen to sign Anelka for some time now to compensate for the departure of Ivory Coast internationals Didier Drogba and Salomon Kalou to the African Cup of Nations.
Avram Grant will be without leading scorer Drogba and Kalou for about a month, and with Andriy Shevchenko injured and Claudio Pizarro in unconvincing form, the club have been left short in attack as they challenge for the Premier League and Champions League.
Anelka, who signed a new four-year contract at Bolton in August, has scored 11 goals this season.
The former Paris Saint-Germain, Arsenal, Real Madrid, Liverpool, Manchester City and Fenerbahce forward cost Bolton £8m back in 2006.
His move to Chelsea makes him the most expensive player in the world, based on cumulative transfers.
Juan Sebastien Veron previously held the record, but Anelka's latest big-money move means he has now cost clubs a staggering £84.8m throughout his career.
The Frenchman was previously third on the all-time transfer fee list, but now moves above Veron and Hernan Crespo as the most valuable player on the planet.
