Flag-waving supporters sang and danced to mariachi music late into the night after the former Mexico City mayor won Sunday's election by a landslide, the magnitude of which spooked financial markets.
Addressing cheering crowds, the 61-year-old ruling party candidate thanked the "millions of Mexican women and men who decided to vote for us on this historic day."
Maria Fernanda Vela, 27, said it was "an inspiration that in such a male chauvinist country, a woman has taken the top job. It fills your heart with pride."
China congratulated Sheinbaum on Tuesday with foreign ministry spokeswoman Mao Ning calling Mexico "a significant power" in Latin America while hailing the "positive trend of development" in the two countries' ties.
US President Joe Biden welcomed Sheinbaum's "historic election" and said he looked forward to working with her "in the spirit of partnership and friendship."
Canadian Prime Minister Justin Trudeau, another key North American ally, also offered congratulations and said he was ready to work closely with Sheinbaum to further strengthen relations.
Brazilian President Luiz Inacio Lula da Silva, a fellow leftist, hailed a "victory for democracy" and vowed to deepen economic ties between Latin America's two biggest economies.
Russian President Vladimir Putin and Ukraine's Volodymyr Zelensky were among other leaders offering congratulations.
- Opposition complains -
Sheinbaum, a scientist by training, won around 59 percent of votes with more than 93 percent of ballots counted, according to the National Electoral Institute.
That was more than 30 percentage points ahead of her main opposition rival Xochitl Galvez, and nearly 50 percentage points ahead of the only man who ran, centrist Jorge Alvarez Maynez.
Galvez, who conceded defeat after initial results were announced, complained Monday that the opposition had faced "unequal competition against the entire state apparatus dedicated to favoring its candidate."
She expressed confidence in the official results but vowed to challenge the outcome, without specifying how.
Mexican women cheered the breaking of the highest political glass ceiling in a nation where around 10 women or girls are murdered every day.
"Our society is violent, sexist, misogynistic -- and Dr. Sheinbaum as president will really be able to help change not only the laws but society," said Lol-Kin Castaneda, 48, who waited late into the night to hear the winner speak.
Nearly 100 million people were registered to vote in the world's most populous Spanish-speaking country, home to 129 million people.
Sheinbaum owes much of her popularity to outgoing President Andres Manuel Lopez Obrador, a fellow leftist and mentor who has an approval rating of more than 60 percent but is only allowed to serve one term.
Lopez Obrador, who will hand over the presidency in October, hailed his protege's victory as a "historic event."
- Election violence -
But this year's election season was particularly violent, with more than two dozen aspiring local politicians murdered.
The bloodshed continued after the polling and as Sheinbaum's victory was being celebrated.
A woman mayor in a western Michoacan state was killed Monday, barely 24 hours after results were released, and a mayoral candidate was killed in the country's south late Sunday, authorities said.
More than 450,000 people have been murdered and tens of thousands have gone missing in Mexico since the government deployed the army to fight drug trafficking in 2006.
Sheinbaum will also have to manage delicate relations with the neighboring United States, in particular trade and the vexed issues of cross-border drug smuggling and migration.
Financial markets reacted nervously to the size of Sheinbaum's win and the potential for a supermajority for her Morena party in Congress, which would make radical reforms easier.
"Morena's landslide victory means fewer checks and balances, increasing institutional and regulatory risks," said analyst Arantza Alonso at risk intelligence company Verisk Maplecroft.
The Mexican stock market closed down around six percent Monday, while the peso fell sharply against the dollar, giving back some of the gains that in recent years saw it nicknamed the "super peso."
Investors were worried the new administration would change the constitution and also undermine the central bank's autonomy, said Gabriela Siller, head of economic analysis at the financial group BASE.
In an apparent attempt to calm the jitters, Sheinbaum announced that Finance Minister Rogelio Ramirez de la O had agreed to stay on in the key position to ensure "good financial and economic management."
"We're going to act with dialogue, harmony and great responsibility," she said in a video published on social media.
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