Foster daughter Namita Kaul Bhattacharya lit the pyre as cries of "Atal Bihari Amar Rahe" reverberated.
President Ram Nath Kovind, Prime Minister Narendra Modi, Congress president Rahul Gandhi and former prime minister Manmohan Singh were among the thousands of people at the Rashtriya Smriti Sthal on the banks of the Yamuna, the BJP patriarch's final resting place.
In keeping with the military honours, three service chiefs placed wreaths on the body of Vajpayee before leaders paid their floral tributes.
The tricolour that was wrapped around Vajpayee's body was removed and given to his foster granddaughter Niharika after which the body was handed over to the family for last rites.
Several foreign dignitaries, including the king of Bhutan and Bangladesh's foreign minister, were also present.
The former prime minister was accorded a state funeral with thousands of people joining his last journey.
The country observed a seven-day state mourning as a mark of respect for the leader was decorated with Bharat Ratna and was very popular. The tricolour is flying half-staff.