The striker became Avram Grant’s first capture at Stamford Bridge and signed a three-and-a-half-year contract.
He had spent two years at Bolton and had already scored 11 goals in 22 games that season before Chelsea became the eighth club of his career.
“I want to tell the Chelsea fans that I see this as a great opportunity and an honour and I will not disappoint them,” Anelka told the Chelsea website.
“Chelsea is the team I really wanted to join and I hope this will be the last club that I play for.
“I am really looking forward to working with Avram (Grant) and Chelsea’s style of football really suits my game.”
Anelka scored 59 goals in 185 games for Chelsea and won the Premier League and two FA Cups as well as the Golden Boot in 2008-09.
But he also missed the decisive penalty in Chelsea’s Champions League final shoot-out defeat to Manchester United in 2008.
Anelka handed in a transfer request in December 2011 while Andre Villas-Boas was in charge.
He left for an 18-month spell at Shanghai Shenhua and also had a loan stay at Juventus.
Anelka returned to England with West Brom in 2013 but his time at Albion ended in controversy after he was sacked by the Baggies a year later.
Anelka was banned for five games and fined £80,000 by the Football Association for making a quenelle sign after scoring against West Ham in December 2013. Anelka denied his use of the sign was anti-Semitic.
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