The two-day official visit, on the invite of Prime Minister Narendra Modi, will see the two leaders discuss regional security, peace and economic development.
President Rajapaksa was welcomed by Minister of State, Gen (retd) VK Singh as he touched down in New Delhi.
"A civilisational relationship nurtured through millennia. President @GotabayaR Aon his first overseas visit since assuming office arrives in India on a State visit at PM @narendramodi's invitation, demonstrating the strength & dynamism of India-SriLanka relations.#NeighbourhoodFirst", tweeted MEA spokesperson Raveesh Kumar.
Before emplaning for India, the Sri Lankan President had tweeted: "Leaving for my first state visit to India and looking forward to strengthening bilateral relations with Shri @narendramodiAand Govt of India."
The team accompanying him includes: Secretary to the Sri Lankan President P.B. Jayasundara, Foreign Secretary Ravinatha Aryasinha, Treasury Secretary S.R. Attygalle, President's advisor Lalith Weerathunge and President's Private Secretary Sugeeshwara Bandara.
India is keen to engage with the Rajapaksas, President Gotabaya Rajapaksa and his brother Prime Minister Mahinda Rajapaksa, who are perceived to be China-leaning.
However, in what could come as a relief to India, Gotabaya Rajapaksa had said on November 18 that his government will maintain "equi-distant and cordial relations with all countries".
"As a policy, we will maintain an equi-distant and yet, cordial relations with all countries and remain neutral in the power struggles amongst nations. I also appeal to all global leaders, to respect the sovereignty and unitary status of Sri Lanka," he had said in a speech.
Keen to build bridges with the new government, India had sent External Affairs Minister S Jaishankar to Colombo soon after the election victory of Gotabaya Rajapaksa. Jaishankar met the new Sri Lankan President and also extended him an invite from Modi to visit India, which he accepted.
Modi, in his congratulatory message, had reiterated India's commitment to continue to work with the Government of Sri Lanka to strengthen ties.
According to the itinerary, Jaishankar will call on the Sri Lankan leader on Friday morning at the ITC Maurya.
After a ceremonial reception at the Rashtrapati Bhavan, Gotabaya Rajapaksa and Modi will hold talks at noon. In the evening he will call on President Ram Nath Kovind. On Saturday the Sri Lankan President will attend events in Delhi and leave in the evening.
Gotabaya Rajapaksa's India visit comes as High Commissioner of India Taranjit Singh Sandhu termed the recently concluded Presidential Elections in Sri Lanka as "a festival of democracy".
Delivering the Lalith Athulathmudali Commemoration Freedom Speech in Colombo, Sandhu said the high-level exchanges underlined the special nature of India-Sri Lanka ties.
He highlighted the strong cooperation between India and Sri Lanka in the field of defence and security, and development partnership. He emphasised that India could offer more in these fields depending on Sri Lanka's own requirements.
The High Commissioner noted that India and Sri Lanka have a lot to offer to each other, and to the world.
( With inputs from IANS )