On 25 May 2011, Lagarde announced her candidacy to be head of the IMF to succeed Dominique Strauss-Kahn, upon his resignation. Her candidacy received the support of the British, Indian, United States, Brazilian, Russian, Chinese and German governments. The governor of the Bank of Mexico (and former Secretary of Finance) Agustín Carstens was also nominated for the post. His candidacy was supported by many Latin American governments, as well as Spain, Canada and Australia.
On 28 June 2011, the IMF board elected Lagarde as its next managing director and chairman for a five-year term, starting on 5 July 2011. The IMF's executive board praised both candidates as well-qualified, but decided on Lagarde by consensus. Lagarde became the first woman to be elected as the head of the IMF. Carstens would have been the first non-European. Her appointment came amid the intensification of the European sovereign debt crisis especially in Greece, with fears looming of loan defaults. The United States in particular supported her speedy appointment in light of the fragility of Europe's economic situation.
In public remarks made right after her appointment, Lagarde stated that both the IMF and EU required Greek austerity measures as a prerequisite for further aid. 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." She said of her predecessor that: "The IMF has taken up the challenges of the crisis thanks to the actions of [Managing Director] Dominique Strauss-Kahn and to his team as well." On 25 December 2011, Lagarde argued that the world economy was at risk and urged Europeans to unify in terms of the debt crisis facing the continent.
On 3 August 2011, a French court ordered an investigation into Lagarde's role in a €403 million arbitration deal in favour of businessman Bernard Tapie. On 20 March 2013, Lagarde's apartment in Paris was raided by French police as part of the investigation. On 24 May 2013, after two days of questioning at the Court of Justice of the Republic (CJR), Lagarde was assigned the status of "assisted witness", meaning that she herself was not under investigation in the affair. According to a press report from June 2013, Lagarde was described by Stéphane Richard, the CEO of France Telecom (a former aide to Lagarde when she was finance minister), who was himself put under formal investigation in the case, as having been fully briefed before approving the arbitration process which benefitted Bernard Tapie. Subsequently, in August 2014 the CJR announced that it had formally approved a negligence investigation into Lagarde's role in the arbitration of the Tapie case. On 17 December 2015, the CJR ordered Lagarde to stand trial before it for alleged negligence in handling the Tapie arbitration approval. In December 2016, the court found Lagarde guilty of negligence, but declined to impose a penalty.
The fashion magazine Vogue profiled Lagarde in September 2011.
Lagarde was portrayed by actress Laila Robins in the 2011 HBO television drama Too Big to Fail, which was based on the popular book of the same name by The New York Times journalist Andrew Ross Sorkin.