Materazzi, who was the head coach of Chennaiyin FC in the first three seasons of the Hero Indian Super League, left by mutual consent.
He was player-manager in the first season, making seven appearances as a player, with Chennaiyin finishing top of the league standings before narrowly losing in the semifinals against Kerala Blasters.
Materazzi guided Chennaiyin to the title in the second season as they dramatically came from behind to beat hosts FC Goa 3-2 in the final.
A record-breaking five-game winning run was instrumental in that triumph as Materazzi inspired the players to success from the brink of elimination.
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"We thank Marco for three memorable seasons and wish him the very best for the future. He will forever be a Chennaiyin FC legend and is also guaranteed a place in ISL history. Marco will always be warmly welcomed back in Chennai and especially at the Marina Arena," the Chennaiyin FC co-owners stated in a joint statement.
Marco Materazzi said, "These past three seasons with Chennaiyin has been a great adventure on a sports and human level. I leave the club today grateful to have been given the opportunity to contribute in my own modest way to the shaping of India as a football nation and most of all grateful to have lived firsthand the birth and growth of Chennaiyin FC. Incredible team, incredible fans, incredible India!"