The President appointed Narendra Modi as the Prime Minister as he has been elected leader of the BJP Parliamentary Party and has the majority support in the Lok Sabha.
The President also asked Mr Modi to submit the list of members to be appointed in the Council of Ministers.
The Press Secretary to the President, Venu Rajamony in a statement said, 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.
Talking to reporters after meeting, Mr Modi said that the swearing-in ceremony will be held on Monday evening.
Mr Mukherjee congratulated Modi for BJP's grand victory in Lok Sabha polls.
Earlier, the BJP Parliamentary Party unanimously elected Mr 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.
Later, constituents of 29-party NDA chose Mr Modi as their leader in a meeting at the same venue.