The wrestler-turned-actor, who was also a former Rajya Sabha member, died at his home in Mumbai following a brief illness. He was 83.
According to IANS, the PM described the actor as "a son of the soil", saying: "I am deeply saddened to learn of the passing away of Shri Dara Singh, who has been an inspiration and icon to many generations in our country.
"A self-educated son-of-the-soil, he rose to the heights of the entertainment world, sports arena and public life with humility and grace. His contribution to the Hindi and Punjabi cinema, wrestling and the Upper House of the Parliament will be remembered by millions."
The former wrestling champion was hospitalised on July 7 in a critical condition. He later suffered kidney failure and died as a result of a heart attack and brain clot.
A source close to the family told IANS: "We are preparing for the last rites, and they should be done around 3pm."
Bollywood celebrities including Manoj Kumar, Abhishek Bachchan, Tabu, Rajpal Yadav and Anu Malik are at Dara Singh's residence.
Amitabh Bachchan paid tribute to the actor via Twitter, describing him as "a great Indian and one of the finest humans".
The 'Rustam-e-Hind' title holder is survived by his wife and six children.
His last rites will be conducted at a cemetery in Juhu.