Narendra Modi will be sworn-in as Prime Minister on 26th of this month.
Mr Modi, called on President Pranab Mukherjee today to stake claim for formation of new government.
Talking to reporters after meeting Mr Modi said, the President invited him to form the government and also asked him to submit the list of members to be appointed in the Council of Ministers.
He said the swearing-in ceremony will be held next Monday at 6 pm. Mr Mukherjee congratulated Modi for BJP's grand victory in Lok Sabha polls.
A delegation of 15 members of National Democratic Alliance, NDA, led by Mr Rajnath Singh, BJP President met the President Tuesday afternoon.
A letter stating that Mr Narendra Modi has been elected as Leader of BJP Parliamentary Party, was handed over to the President.
The delegation among others comprised L K Advani, Murli Manohar Joshi, Sushma Swaraj, Prakash Singh Badal, Chandrababu Naidu, Uddhav Thackeray and Ram Vilas Paswan.
Earlier, the BJP Parliamentary Party unanimously elected Narendra Modi as its leader in a meeting at the Central Hall of Parliament.
His name was proposed by party veteran L K Advani and seconded by senior leaders including Murli Manohar Joshi, Venkaiah Naidu, Nitin Gadkari, Sushma Swaraj and Arun Jaitley.
Mr Narendra Modi said that the Lok Sabha election results represents a new hope for the common man.
He dedicated his government for the uplift of the poor, youth, women and deprived.
He said that he would never give an opportunity to look down on what his government would do.
In a 30-minute address to the newly elected MPs he said, as people's representatives, they are not in Parliament to clinch power, but to work for the betterment of people and fulfill their aspirations.
He described Parliament as a temple of democracy and said a government should live for welfare of the poor.
Mr Modi assured people that there is no need for pessimism going by the past bad experience adding that the country has huge potential. He said he does not believe that the previous governments did nothing. He said they deserve appreciation for whatever good they did.
AIR Correspondent reports, touched by L K Advani's reference to him in his address Mr Modi broke down.
Mr Advani had also broken down earlier while embracing Mr Modi moments after party MPs endorsed his proposal to name him their leader.
Later, constituents of 29-party NDA chose Narendra Modi as their leader in a meeting at the same venue.