Mr Modi said Mr Vajpayee's stewardship put India on a fast track to growth.
Atal Bihari Vajpayee created a separate disinvestment department in the finance ministry in 1999 and subsequently made it a ministry under Arun Shourie in 2001, despite opposition.
Students from an art school place flower petals around a painting of former Indian prime ministerAtal Bihari Vajpayee in Mumbai, India, on August 16, 2018.
Vajpayee was one of the few leaders of the BJP to express anguish when hundreds of Muslims were killed rioting in 2002 in the western state of Gujarat, which Modi governed.
Former Indian Prime Minister Atal Bihari Vajpayee died on Thursday at a hospital in New Delhi where he had been undergoing treatment for a kidney ailment since June.
PHD Chamber of Commerce and Industry President Anil Khaitan expressed deep anguish over the passing away of Vajpayee, saying that a vacuum has been created with his death which would be extremely hard to fill.
Vajpayee served as India's Prime Minister three times: for 13 days in 1996, 11 months in 1998 to 1999 and then from 1999 to 2004.
Following the collapse of the Janata Party government led by Morarji Desai, it was Vajpayee who revamped the Jan Sangh as the Bharatiya Janata Party in 1980.
Vajpayee's more than five-decade-long career peaked in the 1990s, when his masterful oratory attracted tens of thousands to his rallies across the country. Despite the best of efforts, we have lost him today,"the statement read".
"Our nation has lost one of our great political leaders who steered our country as Prime Minister to great heights. We will miss him", Gandhi tweeted.
Vajpayee called the 1992 destruction of a 16th-century mosque on a disputed site by Hindu fanatics India's darkest hour. Having enjoyed cordial relations with most of his political opponents, Vajpayee's illness had seen several non-BJP leaders visiting AIIMS and inquiring about his health. In 1995, at the BJP Maha Adhiveshan at the Mahalaxmi Race Course, Advani announced Vajpayee's name as the BJP's prime ministerial candidate, BJP MLA Atul Bhatkhalkar said.