Image caption Christine Lagarde will start her five-year term at the IMF on 5 July

France's Finance Minister Christine Lagarde, 55, has been named the first woman to head the International Monetary Fund (IMF).

Ms Lagarde fought off Mexico's Agustin Carstens for the job, although an IMF statement said that both candidates "were well qualified".

She received backing from America and Europe and key emerging market nations, including China, India and Brazil.

The post became vacant following the resignation of Dominique Strauss-Kahn.

"The results are in: I am honoured and delighted that the board has entrusted me with the position of MD of the IMF!" Ms Lagarde said via Twitter minutes after the announcement.

In a statement, the IMF said that its 24-member board regarded both candidates as highly suitable for the job, but had decided on Ms Lagarde "by consensus".

'Leadership'

Messages of support poured in, with UK Chancellor of the Exchequer George Osborne saying he was "delighted" and French President Nicolas Sarkozy calling it "a victory for France".

Mr Carstens said he had sent Ms Lagarde his "best wishes and full support", adding that he hoped she would "make meaningful progress in strengthening the governance of the institution".

I will make it my overriding goal that our institution continues to serve its entire membership Christine Lagarde, IMF Managing Director

US Treasury Secretary Timothy Geithner said: "Minister Lagarde's exceptional talent and broad experience will provide invaluable leadership for this indispensable institution at a critical time for the global economy."

Although Ms Lagarde is the first woman to become managing director since the IMF was created in 1944, she maintains the tradition that the post is held by a European.

It has been convention that Europe gets the IMF, while an American gets the top job at the World Bank.

Mr Carstens, Mexico's central bank governor, campaigned on a platform that this time the IMF chief should reflect the emergence of developing nations as an economic force.

However, Ms Lagarde toured the world drumming up powerful support in the Middle East, Asia and South America.

Her appointment looked effectively sealed on Tuesday when America and Russia came out in her favour.

Immediate task

In a signal to IMF members who fear she will be overly-focused on Europe, Ms Lagarde said in a statement: "I will make it my overriding goal that our institution continues to serve its entire membership.

Media playback is unsupported on your device Media caption The IMF's David Hawley announces Christine Lagarde's appointment

"As I have had the opportunity to say to the IMF board during the selection process, the IMF must be relevant, responsive, effective and legitimate, to achieve stronger and sustainable growth, macroeconomic stability and a better future for all."

However, when Ms Lagarde begins her five-year term on 5 July, her immediate task will be to deal with the efforts of the IMF and European Union to resolve the Greek debt crisis and prevent contagion to other eurozone economies.

In a television interview minutes after her appointment, Ms 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.

On a day of riots and protests throughout Greece, she said: "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."

Meeting Strauss-Kahn

Mr Strauss-Kahn resigned abruptly on 18 May after being arrested in New York for an alleged sexual assault. He denies the charges.

Ms Lagarde said that following the turmoil of his arrest, she wanted to unify the IMF's staff of 2,500 employees and 800 economists and restore their confidence in the organisation.

She also said she wanted to meet Mr Strauss-Kahn, if permitted to by the US government.

"I want to have a long talk with him, because a successor should talk with their predecessor," Ms Lagarde said during an interview on French television channel TF1.

"I can learn things from what he has to say about the IMF and its teams," she said.

Before becoming France's finance minister in June 2007, she was minister for foreign trade for two years.

Prior to moving into politics, Ms Lagarde, a former champion swimmer, was an anti-trust and employment lawyer in the US.