Bhandari, a three-term former chief minister, was 77. He is survived by wife Dil Kumari Bhandari, a former MP, two daughters and a son.
He breathed his last at a Delhi hospital this afternoon.
Prime Minister Narendra Modi condoled the demise of Bhandari and praised his role in Sikkim's progress.
"Saddened by the demise of Shri Nar Bahadur Bhandari. His contribution towards Sikkim's progress will always be remembered. My condolences," the prime minister's office said in a twitter post.
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He became the chief minister of the tiny Himalyan state for the first time in 1979 on a Janata Parishad ticket and then again in 1984 and 1989 on a Sikkim Sangram Parishad ticket. The founder of the SSP, Bhandari remained its president till his death.
Known as a pragmati and resilient leader, Bhandari was the second chief minister after L D Kazi to hold the reins of the fledgling state which officially became a part of the Indian Union in 1975.
Chief Minister Pawan Chamling condoled the death of Bhandari.
"I am extremely sad and shocked to know about the untimely demise of Shri Nar Bahadur Bhandari. With his passing away, Sikkim has lost a worthy son of the soil whose contribution to the state and its people are unparalleld.