Lagarde is the first woman to lead the lending organization. She replaces Dominique Strauss-Kahn, who resigned last month after being charged with sexually assaulting a New York City hotel housekeeper. Lagarde was opposed by Agustin Carstens, a Mexican central banker whose candidacy never caught fire, even among developing countries.
Lagarde's selection became all but assured when the Obama administration endorsed her earlier Tuesday. Hours later, the IMF's 24-member board voted to appoint her to the position. She had also won support from Europe, China and Russia.
The executive board represents the 187 members of the IMF, which lends to financially troubled countries.
Lagarde's selection will likely provoke protests from developing countries. Under an informal arrangement dating to the end of World War II, a European always leads the IMF and an American runs its sister organization, the World Bank. The United States also names the IMF's top deputy. Developing nations have pushed to open the positions to candidates outside the United States and Europe.
Analysts say Europe and the United States aren't willing to give up their privileges. And key developing countries, such as China, India and Brazil, tend to regard each other as rivals rather than allies. Carstens complained that he was at a disadvantage from the start because European officials moved quickly to close ranks behind Lagarde.
Lagarde, 55, led the Chicago-based law firm Baker & McKenzie before entering French politics in 2005.
Her supporters have argued that a European should lead the fund because Greece, Ireland and Portugal are now among the IMF's biggest borrowers. Lagarde helped lead negotiations for a bailout package last year that combined European Union and IMF funds in a pool to aid highly indebted European countries.
But her record in helping negotiate the deal isn't widely regarded as a strong achievement. Many analysts argue that Europe's leaders have been too timid in responding to the crisis and have been discredited by their failure to solve it for good.
Eswar Prasad, an economics professor at Cornell University and a former IMF official, said Lagarde's biggest challenge will be to show that she doesn't favor European countries.
"She will have to assert her independence from the European position and advance a broader view," Prasad said. "Whether she can cast off the baggage she brings with her is an open and important question."
Greek officials are now calling for a second bailout package to be completed by the fall, even though Greece has failed to make promised deficit cuts.