Ghani arrived in India on Monday night on a three-day state visit, his first after becoming president seven months ago.
He was received at Palam airport by Minister of State for Finance Jayant Sinha.
Sushma Swaraj called on him at the Dwarka Suite of Rashtrapati Bhavan.
Earlier, Ghani was accorded a ceremonial welcome at Rashtrapati Bhavan.
Ghani is to later proceed for Hyderabad House for talks with Modi.
Both sides will make media statements. Ghani will later be called on by several union ministers, including of Commerce and Industry Minister Nirmala Sitharaman, Defence Minister Manohar Parrikar and Health Minister J P Nadda.
Vice President Mohammad Hamid Ansari will also call on him.
In the evening, he will deliver the keynote address at the Indian Council of World Affairs.
He will also call on President Pranab Mukherjee and attend the presidential banquet.
On Wednesday, Ghani will hold a business meeting with the India business organisations, CII, FICCI and ASSOCHAM. He leaves on Wednesday evening.