Mr Naidu, who was flanked by Prime Minister Narendra Modi and party veteran L K Advani when he filed his nomination in the parliament complex, said the candidature was an "honour" for him and he would uphold the dignity of the office if elected.
In a "farewell" press conference soon after he filed his nomination, he expressed his gratitude to the prime minister and BJP chief Amit Shah as he played down reports that he was not very keen for the new responsibility.
"The office of the vice president has been held by the illustrious people like Sarvepalli Radhakrishnan, Zakir Hussain, M Hidayatullah, R Venkataraman, Shanker Dayal Sharma and Bhairon Singh Shekhawat...," he added.
"I am fully aware of the august responsibilities associated with the office. I would like to assure the people of the country that, on being elected, I will uphold the traditions and standards set by the worthy predecessors. I will uphold the dignity of the office of the vice president," he told reporters.
India's beauty and strength lie in its parliamentary democratic system, Mr Naidu said, adding that it would be his endeavour to strengthen this further.
The former union minister recalled his humble beginnings and likened the BJP to his mother.
Having lost his mother at a very young age, he grew up with party workers and had reached where he had due to the party's support, Mr Naidu said.
But he now no longer belongs to the BJP, he said. "I am above any party now."
Sources close to him later said Mr Naidu had resigned from the party. He had resigned from the cabinet last night after his candidature was announced.
He said he would continue as a member of the Rajya Sabha and cast his vote in the vice presidential poll next month.
Mr Naidu's win is all but certain due to the NDA's numerical superiority over opposition parties, which have fielded Gopalkrishna Gandhi as their nominee.
Members of allies like TDP, Shiv Sena and LJP besides those of AIADMK and TRS, two parties outside the NDA fold but supporting Mr Naidu's candidature, were among the leaders who accompanied Mr Naidu as he filed his nomination.
Top leaders, including Prime Minister Narendra Modi, union ministers and allies like Ram Vilas Paswan, were among the proposers and seconders of his nomination.