The International Monetary Fund on Tuesday chose French finance minister Christine Lagarde to be its next managing director, maintaining Europe’s long-standing hold on the agency’s top job and appointing the first woman to take over the global financial powerhouse.

In a release, the fund’s 24-member executive board said it had chosen Lagarde “by consensus” over Mexican central bank governor Agustin Carstens.

Lagarde, 55, a lawyer well-regarded for her political acumen, takes over an agency at the center of crisis discussions in Greece. It needs “healing” internally as well, Lagarde said in her public statement to the board, after the arrest of former managing director Dominique Strauss-Kahn on sexual assault charges in New York.

Her five-year term will begin July 5.

Any remaining mystery in the campaign to run the agency ended on Tuesday morning when the United States announced it would back Lagarde’s bid, breaking the Obama administration’s silence on the freighted decision just as the IMF board prepared to meet.

A former chairman of the Baker & McKenzie law firm, Lagarde will take over a global institution that is playing an increasingly central role in managing the world economic crisis, with tens of billions of dollars in loans outstanding and supporting credit lines available to keep countries out of trouble.

Lagarde played a central role in crafting an initial round of plans to help Greece as a representative of the French government. She’ll now be renegotiating much of that as head of the IMF.

In her statement to the board, released publicly, she assured members that she would not be an easy touch for European nations that need help. France shares the euro currency with Greece and other troubled European economies that are under the IMF’s watch, and its banks and other major institutions have a direct interest in the outcome of ongoing crisis talks.

“If elected, I will have but one thing in mind when it comes to providing support to a euro-area member: ensuring full consistency with the Fund’s mission and providing for good stewardship of the Fund’s resources,” Lagarde said. “I will not shrink from the necessary candor and toughness in my discussions with the European leaders, on the contrary.”

She also noted the “open wounds” left at the agency following Dominique Strauss-Kahn’s arrest on sexual assault charges, and said that the IMF must now prove it “is not only leading in terms of expertise, but also in terms of integrity and work ethics. We must consolidate and, if needed, restore staff pride in working at the IMF, to get us through the healing process.”

The United States is responsible for more than 17 percent of the roughly $320 billion kitty that runs the International Monetary Fund, and has by far the largest vote on the fund’s board.

Although the United States usually is not shy about exercising its influence, U.S. officials had maintained a studied silence about who they believed should replace Strauss-Kahn, apparently hesitant to weigh in on a global debate about whether the fund should be led by a banker from a non-European country.

At the last minute, with a broad coalition gathering behind Lagarde — including major European powers, African countries, as well as quiet support from Brazil and India — Geithner weighed in.

“I am pleased to announce our decision to support Christine Lagarde to head the International Monetary Fund,” Geithner said in a written statement. “Minister Lagarde’s exceptional talent and broad experience will provide invaluable leadership for this indispensable institution at a critical time for the global economy.”

Russia, which along with China had been hinting it would support Lagarde, said so publicly on Tuesday as well.

Geithner’s statement said the United States was “encouraged by the broad support” Lagarde had secured from IMF member countries, “including from the emerging economies.” It commended Mexican central bank governor Agustin Carstens, who is also vying for the job, “on his strong and very credible candidacy.”

As the competition began, pitting Europe’s long-standing authority to appoint the IMF head with demands from developing nation for more influence, the United States knew that it would offend important allies no matter who it backed.

Side with Lagarde, and the administration would be seen as part of the old-line European axis — earning the enmity of developing nations and contradicting its own promises of reform. Choose Carstens, and the United States would vex close allies in Europe, upend that region’s planning over Greece and other crises, and risk facing opposition to its own traditional prerogatives, such as the choice of a new World Bank president next summer.

Instead, until Tuesday morning, the strategy was to lie low, a stance the Obama administration tried to give a positive spin by saying it was ready to follow the rest of the world rather than play a kingmaker’s role.

Critics, however, argued that neutrality, in this case, was the same as endorsing Lagarde. As a long-shot candidate, and the first credible contender from a developing country, Carstens would have needed a strong push by the United States and other major nations for his candidacy to take hold.

The fund’s 24-member board — whose votes are weighted based on the country or coalition of countries they represent — has said it hoped to choose a new managing director by consensus rather than forcing board members to go on record. The public U.S. endorsement now makes that likely.

The board said it wants to name a new managing director by Thursday, but the decision could be announced after Tuesday’s meeting.

Carstens’s candidacy added elements of actual competition to the process of choosing a replacement for Strauss-Kahn. Considered by some to be technically superior to Lagarde, given a resume that includes prior ranking jobs at the IMF and his current role running Mexico’s central bank, Carstens has been endorsed by Canada, Australia, Mexico and a handful of Latin American nations.

But that backing lagged behind the announced support for Lagarde, a career lawyer and French cabinet minister who joined the competition for the job with the IMF’s version of a home-court advantage. Several of the executive directors were obligated to her by their heads of state and finance ministers before it was even clear who might compete for the post.