Anelka, who has played for Paris Saint-Germain, Arsenal, Real Madrid, Liverpool, Manchester City and Chelsea in the past, was retained by Mumbai after scoring two goals in seven appearances for them in 2014.
The Frenchman's only previous coaching stint came when he was named Shanghai Shenhua's player-manager for a brief period in 2012.
Anelka has already begun putting plans into action and made it clear that his first aim is to ensure Mumbai perform better after finishing seventh last season.
"I would like to say thank you to the Mumbai City staff for giving me the opportunity to coach the club," Anelka told reporters. "We are all very excited to start this new season.
"I'm personally very eager to take on this new role for the club and put a strong competitive team on the pitch! See you very soon."
Meanwhile, Mumbai City co-owner Ranbir Kapoor was delighted that Anelka had agreed to become the team's player-manager and believes that they have a good chance of winning the Indian Super League next season.
"I'm thrilled to have Nicolas as our marquee player-manager," Kapoor said. "Last year he impressed us all with his tactical knowledge and excellent motivational skills.
"It's a role both parties have been discussing for a couple of months and it's been a great start. We will provide Nicolas all the support required to try to win the league this year."