Vienna (CNN) After arduous talks that spanned 20 months, negotiators have reached a landmark deal aimed at reining in Iran's nuclear program.

The agreement, a focal point of U.S. President Barack Obama's foreign policy, appears set to reshape relations between Iran and the West, with its effects likely to ripple across the volatile Middle East.

Representatives of Iran, the United States and the other nations involved in the marathon talks held a final meeting in Vienna on Tuesday.

Obama will hold a press conference on Wednesday in the East Room of the White House to address questions on the agreement.

The president praised the deal on Tuesday morning, saying the agreement met the goals he had in place throughout negotiations.

"Today after two years of negotiation the United States together with the international community has achieved something that decades of animosity has not: a comprehensive long-term deal with Iran that will prevent it from obtaining a nuclear weapon," Obama said from the White House, with Vice President Joe Biden at his side.

"This deal is not built on trust. It's built on verification," Obama said Tuesday.

Iranian President Hassan Rouhani also praised the deal, speaking after Obama finished, as televisions in Iran broadcast the U.S. President's statement live, translated into Farsi.

"Negotiators have reached a good agreement and I announce to our people that our prayers have come true," Rouhani said in a live address to the nation following Obama.

The essential idea behind the deal is that in exchange for limits on its nuclear activities, Iran would get relief from sanctions while being allowed to continue its atomic program for peaceful purposes.

After news of the deal emerged, Yukiya Amano, the chief of the International Atomic Energy Agency, said he had signed a "roadmap" with the Iranian government "for the clarification of past and present outstanding issues regarding Iran's nuclear program."

What's in the deal

The deal reduces the number of Iranian centrifuges by two-thirds. It places bans on enrichment at key facilities, and limits uranium research and development to the Natanz facility.

The deal caps uranium enrichment at 3.67 percent and limits the stockpile to 300 kg, all for 15 years.

Iran will be required to ship spent fuel out of the country forever, as well as allow inspectors from the IAEA inspectors certain access in perpetuity. Heightened inspections, including tracking uranium mining and monitoring the production and storage of centrifuges, will last for up to 20 years.

The U.S. estimates that the new measures take Iran from being able to assemble its first bomb within 2-3 months, to at least one year from now.

Far from over

But the deal between Iran and world powers, brokered during lengthy negotiations in a Vienna hotel, is far from the end of the story.

The accord is expected to face fierce opposition from Republicans in the U.S. Congress, as well as from Israeli Prime Minister Benjamin Netanyahu, a longstanding critic of the negotiations.

"From the initial reports we can already conclude that this agreement is a historic mistake for the world," Netanyahu said Tuesday. "Far-reaching concessions have been made in all areas that were supposed to prevent Iran from obtaining nuclear weapons capability."

When willing to make a deal at any cost, this is the result. From early reports, we can see that the deal is a historic mistake. — בנימין נתניהו (@netanyahu) July 14, 2015

For his part, Obama called Netanyahu on Tuesday to discuss the deal. According to a White House statement, Obama reassured the Israeli leader of his administration's "stalwart commitment to Israel's security."

"The President told the Prime Minister that today's agreement on the nuclear issue will not diminish our concerns regarding Iran's support for terrorism and threats toward Israel," the statement said.

Congress has 60 days to review the agreement, giving its opponents plenty of time to dig into the details and challenge the Obama administration's position.

In Tehran, the deal will need the clear backing of Iran's supreme leader, Ayatollah Ali Khamenei, to fend off any objections from hardliners suspicious of an accord with the United States after decades of hostility and mistrust.

Rouhani said on Twitter that the deal shows that "constructive engagement works."

"With this unnecessary crisis resolved, new horizons emerge with a focus on shared challenges," he tweeted.

#IranDeal shows constructive engagement works. With this unnecessary crisis resolved, new horizons emerge with a focus on shared challenges. — Hassan Rouhani (@HassanRouhani) July 14, 2015

Key players celebrate deal

Speaking ahead of the session, Iranian Foreign Minister Mohammad Javad Zarif called the deal a "historic moment," although he cautioned that it was "not perfect."

Lead negotiators on both sides addressed the press in a joint statement from Vienna on Tuesday morning as well.

U.S. Secretary of State John Kerry praised the Iran nuclear deal reached early Tuesday morning, saying from Vienna that the agreement is a step toward peace and a step away from conflict.

"This is the good deal that we have sought," Kerry said at a press conference, adding that "contrary to the assertions of some," this deal has "no sunset".

Secretary John Kerry ended his statement in Vienna praising Obama "who had the courage to launch this process, believe in it, support it, encourage it, when many thought the objective was impossible, and who led the way from the start to the finish."

EU foreign policy chief Federica Mogherini said Tuesday. She added, "Under no circumstances will Iran ever seek, develop or acquire nuclear weapons" and promised to release full details of the agreement on Tuesday.

There was even a moment of levity that drew some limited laughter from the press conference. When Zarif announced with a smile that he was about to read in Persian the same statement Mogherini had delivered in English, he added "Don't worry, it's the same thing."

Leaders of the Western nations involved in the talks have backed a deal as the best way to stop Iran from becoming a nuclear power.

Iran, meanwhile, has been eager to get rid of international economic sanctions that have been squeezing its economy.

"It's a good day for diplomacy, it's a good day for compromise, it's a good day for a new beginning between Iran -- a pivotal state in the Middle East -- and the United States," said Fawaz Gerges, professor of Middle East studies at The London School of Economics.

Two years of negotiations

It's an agreement roughly two years in the making.

Diplomats from the United States, the UK, France, China, Russia and Germany have been negotiating with the Iranians since 2013.

The official talks began after the election in Iran that year of Rouhani, widely seen as a reformer. He seemed open to warmer ties with the West and said he would work to end international sanctions.

Discussions in November 2013 led to an interim deal called the Joint Plan of Action that offered some sanctions relief in exchange for curbs on Iran's nuclear program, pending further talks toward a permanent solution.

Three months ago, negotiators made a further breakthrough, settling on a framework deal that established the broad principles for the final agreement.

The talks in recent weeks to reach a comprehensive deal had stretched way past their original deadline of June 30. As recently as late Monday, sticking points remained, including Iran's insistence on the lifting of an embargo on the sale of conventional weapons and missiles, multiple sources said.