The package includes freezing Iran's ability to enrich uranium at a maximum 5 percent level, which is well below the threshold for weapons-grade material and is aimed at easing Western concerns that Tehran could one day seek nuclear arms.
Obama hailed the pact's provisions, which include curbs on Iran's enrichment and other projects that could be used to make nuclear arms, as key to preventing Iran from becoming a nuclear threat.
''Simply put, they cut off Iran's most likely paths to a bomb," he told reporters in Washington.
For Iran, keeping the enrichment program active was a critical goal. Iran's leaders view the country's ability to make nuclear fuel as a source of national pride and an essential part of its insistence at nuclear self-sufficiency.
Giving up too much on the enrichment program would have likely brought a storm of protest by Iranian hard-liners, who were already uneasy over the marathon nuclear talks and Rouhani's outreach to Washington.
In a nationally broadcast speech, Rouhani said the accord recognizes Iran's "nuclear rights" even if that precise language was kept from the final document because of Western resistance.
"No matter what interpretations are given, Iran's right to enrichment has been recognized," said Rouhani, who later posed with family members of nuclear scientists killed in slayings in recent years that Iran has blamed on Israel and allies.
Saying "trust is a two-way street," Rouhani insisted that talks on a comprehensive agreement should start immediately.
Iranian Foreign Minister Mohammad Javad Zarif, who led his country's delegation, called on both sides to see the agreement as an ''opportunity to end an unnecessary crisis and open new horizons."
But initial reaction in Israel was strongly negative. Israel's prime minister, Benjamin Netanyahu, called the deal, a "historic mistake."
Speaking to his Cabinet, Netanyahu said Sunday that Israel is not bound by the deal and reserves the right to defend itself. That is a reference to possible military action against Iran.
Netanyahu has said the international community is giving up too much to Iran, which it believes will retain the ability to produce a nuclear weapon and threaten Israel.
U.S. Secretary of State John Kerry, who joined the final negotiations along with the foreign ministers of Russia, China, France, Britain and Germany, said the pact will make U.S. allies in the Middle East, including Israel, safer reducing the threat of war.
"Agreement in Geneva," he tweeted. "First step makes world safer. More work now."
The deal marks a milestone between the two countries, which broke diplomatic ties 34 years ago when Iran's Islamic revolution climaxed in the storming of the U.S. Embassy in Tehran. Since then, relations between the two countries had been frigid to hostile.