The 51-year-old, who was part of the Croatia team who finished third at the 1998 World Cup in France, will succeed Stephen Constantine in the role.
Stimac's biggest achievement on his coaching resume is helping Croatia qualify for the 2014 World Cup in Brazil and his last assignment was with Al-Shahania Club in Qatar.
"Igor is the right candidate to coach the Blue Tigers," All India Football Federation (AIFF) President Praful Patel said in a statement.
"Indian Football is going through a transition, and I am confident his vast experience will guide us to higher echelons."
India are currently ranked 101 in the world by FIFA but broke into the top 100 last years under Constantine, who did not seek an extension after India's exit from the Asian Cup group stages earlier this year.
India has a population of 1.3 billion but the cricket-mad nation is a massive underachiever on the football field. The national side are yet to play at a World Cup.
AIFF's technical committee made an unanimous recommendation to appoint Stimac, whose first assignment with be the Kings Cup in Thailand in June.
"Indian Football would benefit immensely under Igor Stimac," AIFF general secretary Kushal Das said.
"His credentials as a coach, and experience as a player are sure to add immense value to the players, and the Indian Football ecosystem. The momentum gained needs to be sustained."
(Reporting by Sudipto Ganguly; editing by Amlan Chakraborty)
