Vajpayee's party said on Thursday that he would hand his resignation to President A.P.J. Abd al-Kalam at the ornate presidential palace, and his office said he would later address the nation on state-run television.
Vajpayee was driven to his last appointment as the head of this country of one billion people in a white, Indian-made Ambassador car, part of a caravan filled with aides, police and army security guards.
No official announcement was immediately made, but Press Trust of India and other news media reported that Vajpayee had quit.
When the new Parliament convenes, possibly next week, Vajpayee will remain the leader of the National Democratic Alliance of 11 parties with whom he governed and fought the election, his defence minister, George Fernandes, said.
India's oldest party, the Congress, virtually written off by political pundits and rivals, made a stunning comeback in national polls under the leadership of its Italian-born chief Sonia Gandhi.
Results of India's staggered polls showed the party and its allies sweeping the ruling Bharatiya Janata Party (BJP) and its coalition partners from power.
The last Congress government completed its tenure in 1996.
Formed in 1885, the Congress party, which spawned India's apostle of peace Mahatma Gandhi and first prime minister Jawaharlal Nehru, was at the forefront of the campaign to free the country from British rule.