The veteran leader, who was also credited for a landmark nuclear deal with the United States, died late on Thursday at age 92.
Singh's body was taken on Saturday morning to the headquarters of his Congress party in New Delhi, where party leaders and activists paid tributes to him and chanted "Manmohan Singh lives forever".
Abhishek Bishnoi, a party leader, said Singh's death was big loss for the country.
"He used to speak little, but his talent and his actions spoke louder than his words," he said.
Manmohan Singh is credited with changes that reformed India's economy. (AP PHOTO)
Later, Singh's body was taken to a crematorium ground for his last rites as soldiers beat drums.
Government officials, politicians and family members paid their last respects to Singh, whose casket was adorned with flowers and wrapped in the Indian flag.
Security personnel honoured him with a ceremonial gun salute.
Indian President Draupadi Murmu and Prime Minister Narendra Modi, who called Singh one of the country's "most distinguished leaders", and several cabinet ministers took part in the funeral ceremony.
Singh's body was then transferred to a pyre as religious hymns played and cremated.
Authorities declared a seven-day mourning period and cancelled all cultural and entertainment events during that time.
A mild-mannered technocrat, Singh was prime minister for 10 years and leader of the Congress party in Parliament's upper house, earning a reputation as a man of great personal integrity.
He was chosen to be prime minister in 2004 by Sonia Gandhi, the widow of assassinated Prime Minister Rajiv Gandhi.
Singh was re-elected in 2009, but his second term was clouded by financial scandals and corruption charges over the organisation of the 2010 Commonwealth Games.
This led to the Congress party's crushing defeat in 2014 national elections by the Hindu nationalist Bharatiya Janata Party under the leadership of Narendra Modi.
Singh adopted a low profile after relinquishing the post of prime minister.
As finance minister, Singh in 1991 instituted reforms that moved India away from a socialist-patterned economy and toward a capitalist model in the face of a huge balance of payments deficit, skirting a potential economic crisis.
Singh was the first Sikh to hold the country's top post and made a public apology in parliament for the 1984 Sikh Massacre in which some 3000 Sikhs were killed after then-prime minister Indira Gandhi was assassinated by her Sikh bodyguards.
In a move hailed as one of his biggest achievements apart from economic reforms, Singh ended India's nuclear isolation by signing a deal with the US that gave India access to American nuclear technology.
But the deal hurt his coalition government, with Communist allies withdrawing their support and criticism of the agreement growing within India in 2008 when it was finalised.
