He was 85. He is survived by four daughters.
He breathed his last at about 9:30 AM at the city's Combined Medical Institute (CMI).
Official sources said Swami, who became the first CM of the north Indian state when it was created out of Uttar Pradesh in 2000, will be cremated with state honours at 4 PM at Lakhibagh in the city.
His mortal remains have been kept at his ancestral home here for people to pay their last respects. The funeral procession will start at 2 PM, family sources said.
Proceedings in the state Assembly were adjourned for the day after paying condolences to Swami.
Describing his death as a personal loss, Chief Minister Vijay Bahuguna said Swami was an inspiring leader to whom he often went to seek guidance.
Leader of Opposition in the state Assembly Ajay Bhatt said as chief minister of Uttarakhand, Swami gave total freedom to his ministers to work in the interest of people.
Swami represented Dehradun seat in Uttar Pradesh Assembly and was also a member of the neighbouring state's Legislative Council in 1984, 1990 and 1996.
Born at Narnaul in Haryana on December 27, 1927, Swami was a lawyer and social worker before joining politics.
