Khurana (82) is survived by his wife, a son and two daughters. Another son of his had died last month.
A Bharatiya Janata Party (BJP) veteran, Khurana was the chief minister of Delhi from 1993 to 1996 and was appointed the governor of Rajasthan in 2004.
His son, Harish Khurana, said his father breathed his last at his Kirti Nagar residence at around 11 pm Saturday.
"Sad to hear of the passing of Shri Madan Lal Khurana. As Chief Minister of Delhi, Governor of Rajasthan and Union Minister, he contributed immensely to public life and particularly to the well-being of the national capital and its people (sic)," Kovind said in a tweet.
Vice President Naidu also condoled the death of Khurana.
"Deeply saddened by demise of former Chief Minister of Delhi, Shri Madan Lal Khurana. He will be remembered for his immense contribution for growth & development of Delhi. My heartfelt condolences to his bereaved family members and pray for his soul rest in peace. #MadanLalKhurana," he tweeted.
Modi said Khurana worked tirelessly for the progress of Delhi.
"Anguished by the passing away of Shri Madan Lal Khurana Ji. He worked tirelessly for the progress of Delhi, particularly towards ensuring better infrastructure.
"He distinguished himself as a hardworking and people-friendly administrator, both in the Delhi government and Centre," the prime minister tweeted.
In another tweet, he said, "Shri Madan Lal Khurana Ji will always be remembered for the manner in which he strengthened the BJP in Delhi. He made unwavering efforts towards serving the post-partition refugees in Delhi. My thoughts and solidarity with his family and supporters."
Khurana's last rites would be performed Sunday, his family members said.
"Learnt of the unfortunate demise of former Delhi chief minister and BJP leader Madan Lal Khurana. He will be remembered as an ideal swayamsevak and a dedicated Vidyarthi Parishad worker and a strong pillar of the Jan Sangh and the BJP," BJP chief Amit Shah tweeted in Hindi.
Lt Governor Anil Baijal and Delhi Chief Minister Arvind Kejriwal also expressed grief on Khurana's death.
In a tweet, Union minister Dharmendra Pradhan said, "Deeply pained to hear about the demise of Former Chief Minister of Delhi and veteran leader Madan Lal Khurana ji. My condolences to the bereaved family and prayers for the departed soul."
Defence Minister Nirmala Sitharaman too condoled the demise of the former Delhi chief minister.
"Condolences on the passing away of Shri. Madanlal Khurana, former CM of Delhi. May God give strength to his family, @HarishKhuranna and all party workers to bear with this loss," she tweeted.