The 32-year-old will join Shenhua in January, the club said in a statement on its website.
Chelsea confirmed in a statement that they had "agreed terms for the permanent transfer of Nicolas Anelka in the January transfer window."
Shanghai, who finished 11th in the league last season, have also been linked with Didier Drogba, Anelka's team mate at the English Premier League side.
Several Chinese clubs have reportedly contacted Ivory Coast international Drogba about a possible transfer. Last month Drogba refused a one-year extension to his contract at Chelsea and the 33-year-old's deal at the London club expires next year.
Local media have reported that former Arsenal and Real Madrid striker Anelka's lucrative contract would involve both football and commercial cooperation.
While the signing of Anelka may signal an upswing for the sport in the country, Chinese football has lurched from crisis to crisis in recent years and disaffected fans have turned away from the game amid corruption scandals, match-fixing and violence on and off the pitch.
The national team has qualified for the World Cup finals only once when they played in the 2002 edition held in South Korea and Japan but lost all their group matches and failed to score a goal.
In January, they exited the 16-team Asian Cup at the first hurdle after finishing third in their group behind Uzbekistan and hosts Qatar.
Anelka scored 59 goals for Chelsea since arriving from Bolton Wanderers in January 2008.
