The 75-year-old Dalmiya, who was admitted to the city's B M Birla Hospital on Thursday night, is survived by his wife Chandralekha, daughter Vaishali and son Abhishek.
Dalmiya's death plunged the cricket fraternity into grief and Dhoni and Kohli also tweeted their tributes.
"Respect to Mr Dalmiya for his contribution in Cricket.May his soul Rest in Peace.Strength and warmth to his loved ones!" said Dhoni.
"Saddened to hear the news about Dalmiya Ji's demise. Heartfelt condolences to his family and friends," added Kohli.
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Former skipper Anil Kumble too lauded Dalmiya's contribution to the game.
"Saddened by Mr. Dalmiya's death. Immense contribution to Indian and world cricket. A huge loss. Always a players man! Condolences to family!" Kumble tweeted.
"Jaggu's vision energy & dedication built Indian crckt into a global powerhouse I can never 4get & recall today our long innings 2gether RIP," added former administrator Inderjit Bindra.