Here are the 10 latest updates on this big story:
Ms Jayalalithaa's body was first taken to her Poes Garden residence from Apollo Hospital, and from there was moved to Chennai's Rajaji Hall, draped in the national flag, where people will pay their last respects. Her funeral will take place this evening.
While Ms Jayalalithaa's body was being moved to her residence, some supporters stormed the barricades outside her residence, prompting the police to push them back using lathis or batons.
A little after 1 am, Finance Minister O Panneerselvam was sworn in as Tamil Nadu's new Chief Minister at the state Raj Bhavan or Governor's residence. Lawmakers from Ms Jayalalithaa's AIADMK had a short while earlier chosen Mr Panneerselvam to lead them in the state assembly.
Mr Panneerselvam, a staunch Jayalalithaa loyalist, had earlier stood in twice as chief minister when she had to step down. After Ms Jayalalithaa was hospitalised in September, Mr Panneerselvam was given charge of the eight ministries she personally supervised and he also chaired cabinet meetings.
A seven-day mourning has been declared in Tamil Nadu. Schools and colleges will be closed for three days.
Prime Minister Narendra Modi and other leaders have expressed grief at Ms Jayalalithaa's death. "Deeply saddened at the passing away of Selvi Jayalalithaa. Her demise has left a huge void in Indian politics," PM Modi tweeted.
Security across the state has been reviewed as a precaution against violent or self-harming protests by lakhs of supporters of Amma or mother as she was known to them. Shops and petrol pumps closed early on Monday, and Chennai roads were deserted.
After local television channels wrongly reported Ms Jayalalithaa's death on Monday evening, violence erupted at the hospital and the police had to use batons to control the crowd of thousands which tried to rush past barricades. The AIADMK had briefly lowered its flag to half-mast at its headquarters, then hoisted it again after the hospital said the local channels' reports were "totally baseless and false."
After the cardiac arrest Ms Jayalalithaa had been put on an ECMO or an Extra-Corporeal Membrane Oxygenation device, a life support system. London specialist Dr Richard Beale, who had flown down earlier to supervise Ms Jayalalithaa's health, had told NDTV that the politician was "on the most advanced level of support" and that her "underlying conditions" complicated her recovery.
Just days ago, Ms Jayalalithaa, who was treated at the hospital for acute lung infection, was moved from the critical care unit of the hospital to a private room fitted with state-of-the-art equipment.
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