Sheinbaum, a climate scientist and former mayor of Mexico City, won the presidency with between 58.3% and 60.7% of the vote, according to a rapid sample count by Mexico's electoral authority. That is set to be the highest vote tally percentage in Mexico's democratic history.
The ruling coalition was also on track for a possible two-thirds super majority in both houses of Congress which would allow the coalition to pass constitutional reforms without opposition support, according to the range of results given by the electoral authority.
Opposition candidate Xochitl Galvez took between 26.6% and 28.6% of the vote, preliminary results showed, and Sheinbaum said Galvez had called her to concede.
"For the first time in the 200 years of the republic I will become the first woman president of Mexico," Sheinbaum told supporters to loud cheers of "president, president."
Victory for Sheinbaum is a major step for Mexico, a country known for its macho culture and home to the world's second biggest Roman Catholic population, which for years pushed more traditional values and roles for women.
Sheinbaum is the first woman to win a general election in the United States, Mexico or Canada.
"I never imagined that one day I would vote for a woman," said 87-year-old Edelmira Montiel, a Sheinbaum supporter in Mexico's smallest state Tlaxcala.
"Before we couldn't even vote, and when you could, it was to vote for the person your husband told you to vote for. Thank God that has changed and I get to live it," Montiel added.
Sheinbaum has a complicated path ahead. She must balance promises to increase popular welfare policies while inheriting a hefty budget deficit and low economic growth.
After preliminary results were announced, she told supporters her government would be fiscally responsible and respect the autonomy of the central bank.
She has vowed to improve security but has given few details and the election, the most violent in Mexico's modern history with 38 candidates murdered, has reinforced massive security problems. Many analysts say organized crime groups expanded and deepened their influence during Lopez Obrador's term.
Sunday's vote was also marred by the killing of two people at polling stations in Puebla state. More people have been killed - over 185,000 - during the mandate of Lopez Obrador than during any other administration in Mexico's modern history, although the homicide rate has been inching down.
"Unless she commits to making a game-changing level of investment in improving policing and reducing impunity, Sheinbaum will likely struggle to achieve a significant improvement in overall levels of security," said Nathaniel Parish Flannery, an independent Latin America political risk analyst.
The ruling MORENA party has also declared its candidate the winner of the Mexico City mayorship race, one of the country's most important posts, though the opposition has disputed that and claims its own nominee won the contest.
U.S. RELATIONS
Among the new president's challenges will be tense negotiations with the United States over the huge flows of U.S.-bound migrants crossing Mexico and security cooperation over drug trafficking at a time when the U.S. fentanyl epidemic rages.
Mexican officials expect these negotiations to be more difficult if the U.S. presidency is won by Donald Trump in November. Trump has vowed to impose 100% tariffs on Chinese cars made in Mexico and said he would mobilize special forces to fight the cartels.
At home, the next president will be tasked with addressing electricity and water shortages and luring manufacturers to relocate as part of the nearshoring trend, in which companies move supply chains closer to their main markets.
Sheinbaum will also have to wrestle with what to do with Pemex, the state oil giant that has seen production decline for two decades and is drowning in debt.
"It cannot just be that there is an endless pit where you put public money in and the company is never profitable," said Alberto Ramos, chief Latin America economist at Goldman Sachs. "They have to rethink the business model of Pemex."
Lopez Obrador doubled the minimum wage, reduced poverty and oversaw a strengthening peso and low levels of unemployment - successes that made him incredibly popular.
Sheinbaum has promised to expand welfare programs, but it will not be easy with Mexico on track for a large deficit this year and sluggish GDP growth of just 1.5% expected by the central bank in 2025.
Lopez Obrador has loomed over the campaign, seeking to turn the vote into a referendum on his political agenda. Sheinbaum has rejected opposition claims that she would be a "puppet" of Lopez Obrador, though she has pledged to continue many of his policies including those that have helped Mexico's poorest.
In her victory speech, Sheinbaum thanked Lopez Obrador as "a unique person who has transformed our country for the better."
But political analyst Viri Rios said she thought sexism was behind criticism that Sheinbaum was going to be a puppet of the outgoing leader.
"It's unbelievable that people cannot believe she's going to be making her own decisions, and I think that's got a lot to do with the fact that she's female," she said.
