Lagarde will become the first woman to head the International Monetary Fund when her five-year term as managing director begins on July 5. She will find herself immediately immersed in efforts by the IMF and European Union to head off a Greek default that could touch off an international crisis.
The executive board, after considering all relevant information on the candidacies, proceeded to select Ms Lagarde by consensus, the IMF said in a statement.
Lagarde, 55, succeeds Dominique Strauss-Kahn, who resigned from the IMF in May to defend himself against charges of sexual assault against a New York hotel maid. French President Nicolas Sarkozy called the news a victory for France. Lagarde said she was deeply honoured.
Minutes after her appointment, Lagarde pressed Greece to move quickly to push through unpopular austerity measures that the IMF and EU have said are a prerequisite for further aid.
If I have one message tonight about Greece, it is to call on the Greek political opposition to support the party that is currently in power in a spirit of national unity, Lagarde said.
Lagardes win over Mexicos Central Bank governor Agustin Carstens was assured after the United States made its support clear, and emerging market economies China, Brazil, India and Russia did the same.
Carstens congratulated Lagarde on her win and said he hoped she would pursue meaningful progress in strengthening the governance of the institution, so as to assure its legitimacy, cohesiveness, and ultimately, its effectiveness.
The US, worried about the possibility of contagion from the Greek crisis, had cautioned that the appointment of the next IMF chief should not be delayed. Minister Lagardes exceptional talent and broad experience will provide invaluable leadership for this indispensable institution at a critical time for the global economy, US Treasury secretary Timothy Geithner said in a statement.
In a convention dating back to the creation of the IMF and World Bank, Europe has always held the top IMF job, while the World Banks top post has always gone to an American.
Developing countries had warned against another US -European stitch-up although some potential candidates from emerging markets decided not to step up because they did not feel they had a fair chance at the job.
The IMF board moved ahead despite lingering concerns about an unresolved legal case in France looking at Lagardes role in a 2008 arbitration payout to a French businessman.
A top French court has put off a decision on the matter until July 8. The IMF may decide not to offer Lagarde a contract until the court makes a final decision, a board source said.