In a statement, India's foreign ministry said the two leaders would meet on June 26 for the first time after Modi arrives in Washington for a two-day visit.
"Their discussions will provide a new direction for deeper bilateral engagement on issues of mutual interest," the ministry statement said.
White House spokesman Sean Spicer later said that Trump wanted the meeting to advance "our common priorities fighting terrorism, promoting economic growth and reforms and expanding security cooperation in it the Pacific region".
"The two leaders will look to outline a common vision for the partnership that's worthy of India's 1.6 billion citizens."
Trump invited Modi to Washington after the Indian leader rang him in January to congratulate the new president on his inauguration.
During the call, Trump underscored that the US "considers India a true friend and partner in addressing challenges around the world".
But this month, in announcing the US withdrawal from the Paris climate deal, Trump singled out India as a major polluter that he said would gain an edge over the US under the agreement -- a charge New Delhi denied.
Modi vowed India, the world's third-largest polluter, would go "above and beyond" its commitments, as Foreign Minister Sushma Swaraj rejected suggestions India acted disingenuously in signing the pact.
Ties between New Delhi and Washington warmed during the Obama years as India sought greater foreign investment and trade ties with Western nations.
But obstacles have already emerged in the early months of the Trump presidency.
A proposed overhaul of H-1B visas -- working permits used by thousands of Indian software engineers to work in the United States -- has caused immense concern.
Modi's flagship "Make In India" policy, designed to reboot local manufacturing and ramp up exports in tandem with foreign investors, could also run aground on Trump's "America first" instincts.
Major US firms such as Walmart and Apple have grown frustrated by regulations and tariffs imposed by Indian authorities as they seek to crack what is a potentially massive market.