The veteran Congress leader was admitted to a hospital in the temple town following a chest pain around midnight but could not be saved, his family said.
Patnaik, a three-time Odisha chief minister, was in Tirupati to attend the convocation ceremony of the Rashtriya Sanskrit University.
A week-long state mourning has also been declared, officials said, adding that the chief minister dropped his programme on the auspicious 'Aksyaya Tritiya' scheduled for the day.
Patnaik's body is being brought to state capital Bhubaneswar; the last rites will be performed in Puri.
A multi-faceted personality known for his contribution towards literature and culture, Patnaik was born on January 3, 1927.
The Congress stalwart became chief minister in 1980 and continued in office till 1989. He bounced back to power in 1995 and remained CM till 1999.
Patnaik was appointed the Governor of Assam in 2009. Earlier, he was also a minister at the Centre.
After completing early education at Khurda High School, Patnaik passed BA in Sanskrit from the Utkal University in 1947 and did MA in Political Science from the Banaras Hindu University in 1949.
Senior Congress leaders, including former chief minister Hemanand Biswal, leader of opposition in Odisha Assembly Narasimha Mishra, and former union minister Bhakta Charan Das mourned his death.