The announcement was made in a statement after the meeting, where climate change was the main focus.
India "has begun its processes to work toward this shared objective" relating to the Paris agreement, the statement read.
While India has not formally ratified it, White House Press Secretary Josh Earnest welcomed the news shortly after the meeting.
"It's my understanding that (this step) represents a more ambitious goal then India had previously laid out in terms of their timing of signing onto the agreement and so we obviously welcome that announcement from the Indian government," Earnest said at the White House briefing Tuesday.
The agreement must be signed and ratified by at least 55 countries responsible for at least 55% of global greenhouse gas emissions.
"In Paris, joining the forces between India and the United States helped forge a historic agreement that can effectively deal with climate change," Obama said after his bilateral meeting with Modi. "We discussed how we can as quickly as possible bring the Paris agreement into force."
He pointed specifically to securing "the climate financing that's necessary for India to be able to embark on a bold vision for solar energy and clean energy" laid out by Modi.
Indian officials recognize how important the climate change issue is to this White House but have some concerns about the continuity of U.S. policy if a Republican wins the White House in November, said Tanvi Madan, director of the India Project at the Brookings Institution.
Officials from both countries have pointed to progress the sides have made on climate change since Obama's visit to New Delhi in 2015, becoming the first sitting U.S. president to visit India twice.
Talking to reporters following their meeting, the two self-described "friends" spoke warmly of each other and their countries' relationship. Following their lunch, Obama also made the rare appearance in seeing the Prime Minister off to his car and waving from the West Wing.
The visit is meant to consolidate and celebrate a bilateral relationship that has grown closer and stronger over the last few years. That closeness is symbolized not just by the apparently warm friendship between the two leaders, but also by a staggering rise in U.S. defense sales to India, which have jumped from $300 million less than a decade ago to $14 billion today.
Obama and Modi also discussed economic relations, security cooperation and cyber security, while the two countries announced that the U.S. Export-Import Bank will work with India toward a deal with Westinghouse to build six nuclear reactors in India.
Officials from both sides have characterized the two leaders as having "chemistry" with each other.
During the President's last trip to India, Modi broke with established protocol and showed up on the tarmac to be the first to greet Obama in India -- and not just with a handshake. Modi pulled the travel-weary commander in chief in for the "bear hug" seen around the world, though like most unplanned hugs in front of a billion-viewer television audience, it was a little awkward.
The warm relationship comes after a period of strain between Washington and Modi. The nationalist Indian leader was a pariah in the United States until two year ago, after he was denied a U.S. visa over his handling of anti-Muslim riots in 2002 when he was chief minister of the state of Gujarat.
Later Tuesday, Modi meets with Secretary of Defense Ash Carter and with the U.S.-India Business Council. Modi has consistently pushed U.S. businesses -- and particularly Silicon Valley -- to invest in his country.
But today, both countries see more shared interests than differences.
"We have seen in recent years greater and closer coordination between U.S. national security officials and Indian national security officials," Earnest told reporters before Modi arrived. "And the President is certainly interested in trying to deepen and strengthen those ties because it would enhance the national security of both our countries."
On Wednesday, the Prime Minister goes to Capitol Hill to deliver the first address to a joint session of Congress by a foreign leader in 2016. Modi is expected to highlight the shared democratic traditions of the U.S. and India, and to emphasize the ways in which India contributes to world economic growth and what Obama likes to call the "rules-based" international order.
Modi will also be feted at a reception hosted by the House and Senate foreign relations committees and the India caucus.
Modi arrived in Washington Monday. He visited Arlington Cemetery to pay his respects, met with the leaders of think tanks and attended an event on the return of stolen antiquities from India.