Koirala's nephews Atul Koirala and Sudhanshu Koirala lit the funeral pyre at the Pashupati Aryaghat.
A Nepal Police contingent formed a guard of honour as the pyre was lit. Nepal Army soldiers also performed a 13-cannon salute in his honour.
The body was kept at the Dasharath Stadium for final tributes before it was taken to Aryaghat for the last rites.
Prime Minister K P Sharma Oli, acting NC president Ram Chandra Paudel, senior leader Sher Bahadur Deuba, Speaker Onsari Gharti Magar, former prime ministers Madhav Kumar Nepal, Jhala Nath Khanal, Prachanda and leaders of other parties were also present during the last rites.
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External Affairs Minister Sushma Swaraj led an all-party delegation here yesterday to pay homage to Koirala saying India had lost a "true friend".
The high-level delegation comprising Congress leader Anand Sharma, JD(U) President Sharad Yadav, CPI(M) General Secretary Sitaram Yechury and National Security Advisor Ajit Doval, paid their last respects to Koirala.
He served as Nepal's 37th prime minister from February, 2014 to October, 2015. He was elected as Nepali Congress president in September, 2010.
After assuming office, Koirala was tasked with formulating the long-delayed Constitution to bring stability to the nation after years of ethnic conflict and abolition of the 239-year-old monarchy.
He was credited with promulgating the country's new Constitution that completed a stalled peace process.
Plans to cremate Koirala at a newly-launched electric crematorium were cancelled after his family expressed a wish to cremate him on a traditional Hindu funeral pyre.