“That’s good news,” Mr. Le Maire told reporters. “We came to an agreement during these two days in Washington about the way in which we will withdraw” those taxes.

Alexandra LaManna,

a U.S. Treasury Department spokeswoman, confirmed an agreement had been reached and said more details are expected to emerge in the coming days.

“This agreement should put an end to tax and trade disputes with our European allies that could hamper economic growth and business investment, and stop unilateral measures to pave the way for implementation of the 136-nation agreement,” she said.

Most of the U.S. attention in the 136-country tax deal reached last week focused on the global minimum tax that is a priority for Treasury Secretary

Janet Yellen

and the Biden administration.

But other nations, including France, the U.K. and Italy, have been keenly focused on the other half of the deal, which gives countries more ability to levy their corporate income taxes on companies that sell to their customers without a significant physical presence. It is partly aimed at increasing the taxes that companies such as

Facebook Inc.

and

Alphabet Inc.

pay outside the U.S.

Countries have been imposing digital taxes outside the corporate income tax as a way to tax those companies. The deal reached last week would expand the taxing powers of countries based on the size of their consumer markets, even if they aren’t typical profit centers or corporate headquarters. In exchange, countries would have to give up their digital taxes.

The U.S., through both the Trump and Biden administrations, has opposed other countries’ digital taxes as unfair and discriminatorily aimed at an industry dominated by American companies. It has imposed retaliatory tariffs but has suspended enforcement as negotiations have continued.

U.S. officials have pressed for the digital taxes’ removal as part of a broader agreement about which countries get to tax which companies’ profits. The challenge is figuring out when that happens.

The U.S. has urged quick removal of the taxes, but European countries have resisted. The statements from France and the U.S. on Thursday don’t offer full clarity on exactly what will happen, though Mr. Le Maire reiterated that France won’t remove its digital tax until the new tax is in force.

Daniele Franco,

the Italian finance minister who was speaking for the G-20 presidency, didn’t suggest much movement soon.

“By the end of 2023 or the beginning of 2024 the [rules] will be operational, and the agreement is that, at that point, the national taxes will be removed,” Mr. Franco said. “Since the beginning, it has been established that the taxes would be removed when a world-wide solution would be implemented. So we expect national, unilateral taxes to be removed by 2024.”

The resolution of tensions between France and the Biden administration won’t necessarily create bipartisan goodwill.

“Countries with DSTs should demonstrate their good faith and suspend collection of the tax while the OECD process is completed,”

Rep. Kevin Brady

(R., Texas), the top Republican on the House Ways and Means Committee, said earlier this week.

Business groups have also been insistent on a faster removal.

One challenge in the stare-down with the U.S. stems from the system that would replace the digital taxes. The new rules would let countries apply their corporate income taxes to companies based partly on where customers are located, instead of solely where corporate value is created.

That is a shift sought by countries such as the U.K., Italy and Spain, which have been frustrated to see technology giants earning profits off their citizens without paying significant corporate income taxes.

The international agreement calls for a multilateral framework to implement those changes, which would upend the network of tax treaties and other rules that have governed the international tax system for decades. The power to tax the largest multinational companies would be replaced by a new formula.

Such an agreement would likely need to go through the U.S. Congress, and Republicans contend that it would require a treaty and thus two-thirds approval in the Senate. That would require the support of at least 17 Republicans in the current alignment. Other countries are well aware of the potential hurdles that the Biden administration would face in getting those votes.

In a letter last week, three senior Senate Republicans said they were concerned by recent suggestions that the administration thought it could implement the changes without changing tax treaties that had been ratified by two-thirds of the Senate.

“Bypassing this process to override our bilateral tax treaties would irreparably erode the exclusive treaty authority the Constitution provides to the Senate,” wrote Republican Sens.

Jim Risch

and

Mike Crapo

of Idaho and

Pat Toomey

of Pennsylvania.

The Biden administration has been more circumspect about the legislative path forward, hinting that there may be ways to implement the agreement without a treaty. No action on this in the U.S. is expected until next year.

Tying the digital-tax removal to the adoption of the multilateral deal could help the administration push the plan through Congress by offering Republicans a reason to back the deal, said

Daniel Bunn,

vice president of global projects at the Tax Foundation, a Washington group that generally favors simpler taxes with lower rates.

But Republicans, he said, will also be concerned about just how much of the U.S. tax base they would be ceding in the broader agreement.

Hans Vijlbrief,

the minister of taxation for the Netherlands, which doesn’t have a digital tax, said other countries know that the changes in dividing up taxing authority are the most politically challenging for the U.S. and are watching the legislative process.

“It’s not that we don’t trust Capitol Hill, but there are other interests there,” Mr. Vijlbrief said in an interview Wednesday. “I would say that the U.S. is good for its word. If they promise that they will do this, I take it as a position that they will do this.”

—Paul Hannon and Sam Schechner contributed to this article.

Write to Richard Rubin at richard.rubin@wsj.com