The fund's board met in the wake of the court decision finding her guilty in a 2008 case dating back to her tenure as French finance minister. It took into account all factors including her "outstanding leadership of the Fund and the wide respect and trust for her leadership globally."
"In this context, the Executive Board reaffirms its full confidence in the managing director's ability to continue to effectively carry out her duties," the board said in a statement.
"The Executive Board looks forward to continuing to work with the managing director to address the difficult challenges facing the global economy."
Lagarde told reporters shortly after the IMF statement that while she was not satisfied with the court decision, she would not appeal.
"There comes a point in time when one just has to stop, turn the page, and move on and continue to work with those who have put their trust in me," Lagarde said. "I will put all my energies and enthusiasm into this role."
She also thanked the board and IMF staff for their support during a "painful" process.
Support from France, US
The French government earlier Monday expressed its confidence in Lagarde continuing at the helm of the IMF, and US Treasury Secretary Jacob J. Lew issued a statement of support immediately after the board decision.
"The United States joins the IMF Executive Board in reaffirming our full support of Managing Director Lagarde," Lew said. "She is a strong leader of the IMF, and we have every confidence in her ability to guide the Fund at a critical time for the global economy."
The French court found Lagarde guilty of negligence over a massive payout to the tycoon Bernard Tapie in 2008, but she will not be fined or face prison, nor will the decision create a criminal record.
The case stemmed from Lagarde's decision in 2007 to allow a dispute over sale of the Adidas sports brand to the state-owned Credit Lyonnais bank to be resolved by a private arbitration panel, and then failing to challenge the result.
The court cleared her of negligence over her decision to refer the matter to arbitration but upheld the charge over her failure to contest the award.
She noted that the public prosecutor had sought to have the charges dismissed.
The case was another instance of controversy surrounding an IMF managing director. Lagarde was named to lead the organization in July 2011 after her predecessor Dominique Strauss-Kahn, also a former French finance minister, was forced to resign amid a sex scandal.
And his predecessor, former Spanish economy minister Rodrigo Rato, is facing prosecution in Spain for embezzlement during his time as a banker.
The first woman to head the IMF, Lagarde presided over some of the worst of the fallout from the 2008 financial crisis and is in her second term as managing director.
She was reappointed in February, despite the ongoing legal troubles.