"I'm pleased to join Mumbai City FC & very exciting in joining Indian Super League. Talented international players & top Indian talent will make matches thrilling affairs," Anelka, a World Cupper, wrote on his twitter handle.
"I look forward to using my ability to do well for my team in the matches we will play," he added.
The former Paris Saint-Germain, Arsenal, Real Madrid and Chelsea striker had been without a club since his controversial exit from West Bromwich earlier this year.
Reports in the British media had claimed that Anelka had signed a contract with Mumbai City FC till the Christmas eve.
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Anelka's agent, last week, had said that the striker was set to join the Indian franchise.
Anelka began his career at Paris Saint-Germain, but soon moved to Arsenal. Real Madrid signed him in 1999, before he returned to Paris Saint-Germain. He transferred to Chelsea from Bolton in 2008.
In June 2010, Anelka was omitted by the French Football Federation from the World Cup squad for comments directed against national coach Raymond Domenech.