Vajpayee represented the UP capital in Lok Sabha several times before being forced by poor health to opt out of public life.
Before filing his nomination, Singh participated in a 'puja' at his residence and in a 'havan' at the BJP headquarters, where he also addressed party workers.
In his brief address, Singh said that there was a wave in favour of the party in the country and "all workers need to work thinking of themselves as Rajnath Singh and exercise restraint."
"We are going to form the government. You have to seek vote and support of every household visiting people of every caste and religion," he added.
