The Sri Lankan leader will also meet President Ram Nath Kovind.
In his first overseas tour after taking reins of Sri Lanka over a week ago, President Gotabaya Rajapaksa arrived in New Delhi on a three-day visit, signalling his intent to deepen bilateral ties with India.
On Friday, Gotabaya Rajapaksa and Prime Minister Narendra Modi will hold extensive talks to explore ways to further expand the already close ties between the two neighbouring countries.
A plethora of issues including fulfilling aspirations of the Tamil community in Sri Lanka, the situation in the Indian Ocean region and steps to boost trade and investment ties are likely to figure in the talks.
Last week, India said it was looking forward to work closely with the new Sri Lankan government and hoped that it would be able to fulfil the aspirations of the Tamil community in that country.
In a tweet, before leaving for New Delhi, Gotabaya Rajapaksa said he was looking forward to strengthening bilateral relations with India.
"Leaving for my first state visit to India and looking forward to strengthening bilateral relations with Shri @narendramodi and Govt of India," he said.
The Sri Lankan leader will also meet President Ram Nath Kovind.
Gotabaya Rajapaksa, a former defence secretary who is credited with ending the country's long civil war, was sworn in as the island nation's new president on November 18, a day after he won the closely fought presidential election in the island nation.
Three days later, he appointed his elder brother Mahinda Gotabaya Rajapaksa as the prime minister.
The newly-elected Sri Lankan President was received at the airport by Union minister V K Singh.
External Affairs Minister S Jaishankar travelled to Colombo last week as a special envoy of Prime Minister Modi to convey his greetings to Gotabaya Rajapaksa.
There have been apprehensions among the minority Tamil and Muslim communities about the new government's policies towards them after the Gotabaya Rajapaksa clan tightened its grip over the country.