Anand, along with his wife Aruna, called on Jayalalithaa at the state secretariat where she complimented the world champion for his achievement.
The Chief Minister had earlier sent a letter to Anand saying that he had brought laurels both to Tamil Nadu and India and announced a reward of Rs two crore.
Describing his meeting with the Chief Minister as "incredibly nice", Anand thanked her for the efforts of the state government in promoting chess among the students.
Thanking Jayalalithaa for the cash reward, Anand also backed the idea of corporate support for chess, saying it will help the sport.
Jayalalithaa had recently said that Anand deserves Bharat Ratna, the country's highest civilian award.
Anand defeated challenger Boris Gelfand of Israel in a tense rapid chess tie-breaker to win the World Championship crown for the fourth time in a row in Moscow on May 30.