WASHINGTON — Over a two-hour breakfast of tea and pastries at the Hotel Amigo in Brussels in July, Treasury Secretary Janet L. Yellen tried to persuade Paschal Donohoe, the Irish finance minister, to abandon Ireland’s rock bottom corporate tax rate and join the global deal the Biden administration was racing to clinch.

The closing pitch was simple: Ireland cannot go back in time. The days of American companies moving their headquarters to Ireland for tax purposes were largely over, and more than 100 countries had already agreed in principle to join the agreement.

That meeting kicked off a three-month push to hash out the most sweeping changes to the international tax system in a century, which culminated in an agreement that President Biden and other leaders of the Group of 20 nations are expected to complete this week in Rome. The deal has become crucial to Mr. Biden’s domestic agenda, with the White House and Democrats in Congress now relying on revenue from a new 15 percent global minimum tax and other changes to help pay for the expansive spending package still being negotiated.

Getting to yes was not easy. In the end, the United States had to convince Ireland that its economy would be better off raising its cherished 12.5 percent corporate tax rate and joining rather than remaining a tax haven and leaving the global tax system under a cloud of uncertainty. With the European Union needing all 27 nations to be on board, the pressure was on to get Ireland to come around.

Officials from countries involved in the negotiations said the outcome was not clear until hours before the Organization for Economic Cooperation and Development announced on Oct. 8 that Ireland and two other holdouts — Estonia and Hungary — had joined the pact.

Nearly 140 countries agreed to adopt a global minimum tax of 15 percent and settled on terms to tax large, profitable multinational corporations based on where their goods and services are sold, rather than where they operate. The agreement aims to end corporate tax havens that have for decades siphoned tax revenue away from governments, leaving infrastructure and public health needs languishing.

“I think the world had come to understand that at the end of the day, all the countries trying to raise tax revenue are the losers, the companies are the winners, and the workers are the losers,” Ms. Yellen said in an interview on Tuesday. “No country really feels it can act independently to raise taxes because its firms will be uncompetitive, so the only way to do this is to hold hands and say enough is enough.”

The deal is a signature achievement for Ms. Yellen, who has spent the past eight months trying to persuade nations to agree on a global tax pact that sputtered during the Trump administration.

The push to reach a deal stemmed from the administration’s concerns about a global race to the bottom on corporate taxation, a phenomenon that was viewed as a big obstacle to Mr. Biden’s plan to increase corporate taxes domestically.

The administration viewed persuading the rest of the world to set a global minimum tax as crucial to its own plans to raise the corporate tax rate to 28 percent, since that would minimize any competitive disadvantage. The Treasury Department estimated that its international tax plans could raise $700 billion in tax revenue over a decade.

To show that the new administration was taking the negotiations seriously, Ms. Yellen told her counterparts in February that she was abandoning a Trump administration stance that would have effectively blocked other countries from imposing new taxes on American companies. She offered a plan that would allow the world’s richest companies, regardless of where they are based, to face new taxes in exchange for the removal of digital services taxes.

“It had been a show stopper in these negotiations that had been going on for many years,” Ms. Yellen said.

The next big obstacle was settling on a rate. The United States wanted a minimum tax of 21 percent, very likely a nonstarter for a country such as Ireland, which has relied on its 12.5 percent tax rate to attract international investment. In May, the United States agreed to continue negotiations on the basis that the rate would be “at least” 15 percent — while hoping to nudge it higher.

“The turning point has been the support of the American administration,” Bruno Le Maire, France’s finance minister, told The New York Times this month.

To get the deal over the finish line, Ms. Yellen relied on two tax experts, Itai Grinberg and Rebecca Kysar, whom she tapped in early February and describes as “invaluable” partners in navigating international negotiations.

Mr. Grinberg, a tax law professor at Georgetown University who worked in the Treasury Department during the Bush and Obama administrations, was initially viewed with skepticism by some progressives, who noted that in 2016 and 2017, he lamented America’s “singularly high corporate tax rate” during congressional hearings and called for the rate to be slashed in favor of a consumption tax.

But in early 2020, Mr. Grinberg wrote in a Foreign Affairs essay that European digital services taxes could open a dangerous front in the Trump administration’s tariff wars and warned that the “decay of the century-long international tax order is likely to accelerate” without a deal. Later that year, Mr. Grinberg alerted Mr. Biden’s campaign advisers on how their international tax proposals meshed with the stalled discussions of a global minimum tax. After the election, he joined Mr. Biden’s transition team.

Ms. Kysar, a professor at the Fordham School of Law and a tax treaty expert, has been a vocal critic of the 2017 Republican tax overhaul. In 2018, she told the Senate Finance Committee that the law’s international tax provisions “fundamentally botched general business taxation.” Ms. Kysar had collaborated on research with David Kamin, deputy director of the White House’s National Economic Council, who helped recruit her to join the transition team and administration.

With the Treasury Department working remotely, Mr. Grinberg and Ms. Kysar spent months juggling Zoom meetings with officials from finance ministries around the world and fielding calls with tax directors from America’s largest companies, which have been anxious about what the agreement will mean for their tax bills.

Working from their basements in Washington and Connecticut, they regularly exchanged emails in real time during negotiations, but they had never met until they traveled to a gathering of finance ministers in Venice in July. At such summits, they would often employ a divide and conquer approach, with Ms. Kysar joining Ms. Yellen in meetings with her counterparts and Mr. Grinberg negotiating separately with Irish tax officials.

The final months of negotiations centered on the United States and Ireland, but with moving parts falling in and out of place from Peru to India, which threatened to back out of the deal shortly ahead the announcement.

Ms. Yellen’s approach with Ireland was to cajole more than to pressure.

“Where once upon a time this tax advantage may have been important to Ireland, Ireland has built a really strong economy with a very well educated labor force,” Ms. Yellen said. “It is an extremely attractive base for American multinationals to choose as their E.U. headquarters.”

In a call with Ms. Yellen in early September, Mr. Donohoe said that the deal hinged on the United States agreeing to drop language suggesting the rate could be higher than 15 percent.

Ms. Yellen signed off on removing the “at least” 15 percent language, yet what Mr. Donohoe would do was still not clear. That was, until Oct. 7, when he called Ms. Yellen and Ms. Kysar to say that Ireland was in.

“Ireland is a country that believes that smaller economies like our own do need to be competitive,” Mr. Donohoe said in an interview. “But we also know that for economies like our own, for societies like our own, we deeply value cooperation, we deeply value compromise.”

To demonstrate American solidarity, Ms. Yellen will visit Dublin next month.

The next steps could be even more challenging. A deal among countries does not mean there is agreement within those nations, including the United States, which will need to change America’s tax code and potentially rewrite tax treaties to comply with the agreement. That could require Republican support, which is not guaranteed. Top House and Senate Republicans have assailed the pact, calling the deal a “surrender.”