He breathed his last at around 9:30 AM at the city's Combined Medical Institute (CMI) where he was admitted a few days back.
Swami, who is survived by four daughters, became the first Chief Minister of the north Indian state when it was carved out of Uttar Pradesh in November 2000.
He remained at the helm till October 29, 2001.
Swami's mortal remains were consigned to flames with full state honours at Lakhibagh here in the presence of a host of political leaders including former BJP Chief Ministers Ramesh Pokhariyal Nishank and Bhagat Singh Koshiyari.
The state government declared a 3-day state mourning and the Legislative Assembly was adjourned for the day as a mark of respect to the departed leader.
Earlier, Swami's body was kept at his ancestral home for people to pay their last respects.
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Chief Minister Vijay Bahuguna and Parliamentary Affairs Minister Indira Hridayesh visited Swami's house and placed wreaths at his body
Leaders from across the political spectrum condoled his death describing Swami as a warm-hearted person who was always available to young members of the House to guide them.
Describing his death as a personal loss, the Chief Minister said Swami was an inspiring leader to whom he often went to seek guidance.
Swami represented Dehradun seat in the Uttar Pradesh Assembly and was also a member of the UP Legislative Council in 1984, 1990 and 1996.
Born at Narnaul in Haryana on December 27, 1927, he was a lawyer and social worker before joining politics.