He is set to be declared elected unopposed on the last day of candidature withdrawal on August 19 as the opposition BJP has decided not to nominate a candidate for the bypoll.
Singh filed four sets of nomination papers in the chamber of returning officer in the Rajasthan Assembly and expressed gratitude to the Congress party for nominating him.
The ruling party, which has a majority in the assembly, is confident on sending him to the upper house.
Singh, 86, arrived here in the morning and spent some time at a hotel before reaching to the assembly for filing nomination papers.
Accompanied by Chief Minister Ashok Gehlot, Deputy Chief Minister Sachin Pilot, AICC general secretary in charge for Rajasthan Avinash Pande, Parliamentary Affairs minister Shanti Dhariwal, chief whip Mahesh Joshi, Health minister Raghu Sharma and others, the former prime minister filed the nomination in the chamber of the returning officer and assembly secretary Pramil Kumar Mathur.
Later, he told reporters that he will do whatever is possible to promote the cause of the people of the state.
He also condoled BJP leader Madan Lal Saini's death in June, which has led to the vacancy in the upper house.
"I am very grateful to the Congress party and Rajasthan Chief Minister Ashok Gehlot, Deputy Chief Minister Sachin Pilot and all members of the Congress party for nominating me to this vacant seat in the council of states," he told reporters after filing the nomination.
Saying he recognised there were circumstances in which the vacancy was created, he conveyed his condolence to Saini's family.
"I express gratefulness to the people of Rajasthan and the Congress party for giving me this privilege for serving the people of Rajasthan in the council of states. I will do my very best to do whatever is possible to promote the cause of the people of Rajasthan," he added.
Pilot said the Rajasthan Congress will benefit from Singh's experience.
"I am happy that the Congress party has made former prime minister Manmohan Singh its candidate for the vacant seat in Rajya Sabha. Manmohan Singh's personality and experience will benefit us all."
"I am happy that all of us Congressmen from Rajasthan, Congress MLAs will get a chance to make a former prime minister an MP," Pilot said.
The Congress has a majority in the state assembly and Singh, thus, is likely to win the bypoll.
The Rajasthan Assembly has 200 seats, but two seats are vacant.
The Congress has 100 MLAs and its alliance partner Rashtriya Lok Dal has one seat, the Bharatiya Janata Party has 72, Bahujan Samaj Party 6, Bharatiya Tribal Party, Communist Party of India (Marxist) and the Rashtriya Loktantrik Party have two seats each, 13 are independents.
The ruling Congress in the state also enjoys the outside support of 12 of the 13 independents and the BSP legislators.
Meanwhile, the opposition BJP held a meeting of its legislators to discuss about the bypoll.
Leader of opposition Gulab Chand Kataria said the opinions of the party MLAs were conveyed to the party high command, which decided not to nominate a candidate.
"The party high command has conveyed us their decision to not nominate a candidate for the Rajya sabha bypoll," Kataria said.
Singh, the veteran Congress leader, was a member of the upper house from Assam for almost three decades.
He was a Rajya Sabha member for five consecutive terms from 1991 to 2019 and the country's prime minister for two consecutive terms between 2004 and 2014.
His tenure in Rajya Sabha ended on June 14 this year and he could not be renominated as the Congress party did not have the strength to send him to the upper house from Assam again and there was no other vacancy left.
Rajasthan has 10 Rajya Sabha seats and one got vacant after the demise of Madan Lal Saini, who was also the state president of the BJP.
The remaining nine seats of Rajya Sabha from the state are with BJP.