Obama made the announcement in a speech to India's parliament on the third and final day of his visit. In doing so, he fulfilled what was perhaps India's dearest wish for Obama's trip here. India has been pushing for permanent Security Council membership for years.
"The just and sustainable international order that America seeks includes a United Nations that is efficient, effective, credible and legitimate," Obama said. "That is why I can say today - in the years ahead, I look forward to a reformed U.N. Security Council that includes India as a permanent member."
The announcement brought the loudest applause of Obama's speech. But it does not mean that India will join the five permanent Security Council members anytime soon. The U.S. is backing India's membership only in the context of unspecified reforms to the council that could take years to bring about.
That makes Obama's announcement more of a diplomatic gesture than a concrete step. Nonetheless, it underscores the importance the U.S. places on fostering ties with this nation of 1.2 billion people, something Obama has been seeking to accomplish throughout his time here.
Obama said repeatedly throughout his three days in India - first in the financial center of Mumbai and then in the capital of New Delhi - that he views the relationship between the two countries as one of the "defining partnerships" of the 21st century. He set out to prove it by making India the first stop on a four-country tour of Asia, and then through economic announcements, cultural outreach and finally the announcement about the U.N. Security Council.
India has sought permanent council membership as recognition of its surging economic clout and its increased stature in world affairs. The U.S. endorsement is certain to deepen the ties between them and could also send Obama's popularity in India skyrocketing to a level comparable to that enjoyed by George W. Bush. The former president is seen as a hero here for helping end India's nuclear isolation.
The five permanent members of the Security Council are the U.S., China, France, the United Kingdom and Russia.
Debate has raged for years over how to change a structure that is widely seen as outdated and it is unlikely to be resolved anytime soon. So it's unclear when India's drive for permanent membership will ever be realized. But backing it at all is a critically important move from India's perspective.
In another important gesture to India, Obama went farther than he had previously during his stay in addressing the terror threat inside Pakistan, India's neighbor and archrival. Obama angered some here when he visited a memorial to victims of the 2008 Mumbai terror attacks but didn't mention Pakistan, which was home to the attackers.
"We will continue to insist to Pakistan's leaders that terrorist safe-havens within their borders are unacceptable, and that the terrorists behind the Mumbai attacks be brought to justice," the president said in the address, to loud applause. "We must also recognize that all of us have an interest in both an Afghanistan and a Pakistan that is stable, prosperous and democratic - and none more so than India."
Muslim-dominated Pakistan and Hindu-majority India have gone to war and remain deeply suspicious of each other. Indian officials accuse Pakistan's intelligence service of helping orchestrate the 2008 Mumbai attacks that killed 166 people and say the country has not done enough to crack down on the Pakistan-based extremists held responsible.
Pakistan views India's ties with the U.S.-backed government in Afghanistan as an effort by its old rival to encircle it.
Throughout his time here, Obama has taken pains to cast his visit as a search for U.S. jobs and benefits to people back home, sensitive to the priorities of U.S. voters who punished the Democratic Party in last week's midterm elections, in part over high unemployment. He touched on the theme again Monday.
"As global partners we can promote prosperity in both our countries," Obama said. "Together, we can create the high-tech, high-wage jobs of the future."
Obama departs early Tuesday for Indonesia, the country where he spent four years as a boy. From there, he heads to South Korea for a meeting of the Group of 20 developed and developing nations, and then to Japan for a gathering of the Asia-Pacific Economic Cooperation forum. He returns to Washington on Nov. 14.