Security clampdown in Kashmir after death of separatist icon
Troops put up barbed wire and barricades on roads leading to Geelani's house in the main city of Srinagar after the family announced the death.
Announcements were made from loudspeakers of the main mosque near Geelani's residence asking people to march towards the house.
But police said no one in the Kashmir valley would be allowed to leave their homes. Thousands of security forces were immediately deployed and mobile internet services were cut across the area.
Scores of armoured vehicles and trucks patrolled main roads in Srinagar.
Geelani was an uncompromising campaigner against Indian rule in the Muslim-majority Himalayan region divided between India and Pakistan since 1947.
He spent years in jail and had been under house arrest for most of the past 11 years. He had been ill for several months with heart and kidney problems.
Pakistan Prime Minister Imran Khan was among the first to pay tribute to Geelani, saying on Twitter that he was "deeply saddened" at the death of the "Kashmiri freedom fighter".
Khan said that Geelani had "struggled all his life for his people and their right to self-determination. He suffered incarceration and torture by the occupying Indian state but remained resolute."
Pakistani cricket legend Shahid Afridi also tweeted in tribute.
"The fight for Kashmir's freedom has taken so many of our elders who have carried the weight of this movement for decades," he wrote. "May we carry on their courage and legacy."
Geelani had been a thorn in India's side since the early 1960s when he began campaigning for the territory's merger with Pakistan. He also pursued his separatist calls as a member of the Kashmir assembly.
The veteran politician was jailed for nearly 10 years after 1962 and often restricted to his home after that.
Since his youth, Geelani had been a member of Jamaat-i-Islami, the largest political-religious organisation in Indian Kashmir that was banned by the Hindu nationalist government in 2019.
He rejected any notion of direct talks with the New Delhi government unless it formally "accepts Kashmir as a disputed territory" and stopped describing the region as an "integral part of India". Governments of all political colours insist on sovereignty over Kashmir.
Geelani was also a staunch critic of the sporadic but failed attempts at dialogue between India and Pakistan -- nuclear-armed rivals that fought two of their three wars since independence over Kashmir and came close to a fourth one in 2016.
His hardline stance also had critics in Kashmir.
Mehbooba Mufti, a former chief minister of Kashmir, said on Twitter: "We may not have agreed on most things but I respect him for his steadfastness and standing by his beliefs."
Kashmir is one of the world's most militarised zones, with 500,000 Indian security forces deployed in the region. Tens of thousands, mainly civilians, have died since an insurgency erupted in 1989.
India has been struggling to bring normal life back to Kashmir after it cancelled the region's semi-autonomous status and divided it into two centrally controlled territories in August 2019.
A security clampdown imposed at the time saw mobile internet services cut for more than a year. Scores of political leaders were detained and many are still not free.
Prime Minister Narendra Modi said the move was intended to bring peace and prosperity to Kashmir. Separatist leaders said it was to punish the Muslim population.