He was received at the airport by Commerce Minister Nirmala Sitharaman.
He will hold talks with Prime Minister Narendra Modi tomorrow during which both leaders are expected to explore ways to further boost bilateral ties besides discussing the fishermen issue.
The proposed comprehensive economic partnership agreement between the two countries and the Tamil ethnic issue are likely to figure in the talks.
External Affairs Minister Sushma Swaraj, Finance Minister Arun Jaitely, Railways Minister Suresh Prabhu, Coal and Power Minister Piyush Goyal, Road Transport and Highways Minister Nitin Gadkari and Oil Minister Dharmendra Pradhan will also meet the Sri Lankan Prime Minister.
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The visit assumes significance as President Maithripala Sirisena also chose India to be his first overseas destination after being elected to office in January.
66-year-old Wickremesinghe was picked by President Sirisena, who handed a shock defeat to Mahinda Rajapaksa in the polls, to lead a minority government in January till the parliamentary elections last month.
The Comprehensive Economic Partnership Agreement is expected to be part of the talks agenda. Prime Minister Modi, during his visit to Sri Lanka in March, had said both countries should move boldly to conclude the pact and attract investments.