Former Mexico City mayor Sheinbaum, 61, won the highest vote percentage in the history of Mexico's democracy, according to preliminary results from the electoral authority.
Her party's victory was so extensive that markets fell on concerns that the ruling coalition would secure a congressional super-majority, which initial results suggested was possible, allowing them to pass controversial constitutional reforms such as in the energy sector unchecked.
Mexico's peso lost as much as 4% against the dollar on Monday, later recovering a bit, trading down 3%. Mexico's stock market was down 3% in morning trade. read more
Sheinbaum secured between 58.3% and 60.7% of votes, according to the INE electoral institute's rapid sample count released late Sunday night.
In her victory speech on Sunday night, Sheinbaum, a physicist who was part of a United Nations panel of climate scientists that received a Nobel Peace Prize in 2007, thanked Lopez Obrador, calling him "an exceptional, unique man who has transformed Mexico for the better."
Lopez Obrador doubled the minimum wage, reduced poverty and oversaw a strengthening peso and low levels of unemployment - successes that made him popular and helped Sheinbaum to victory. But analysts believe Sheinbaum will find it difficult to follow in his footsteps.
"We made history!" Sheinbaum told a crowd early Monday morning in the Zocalo square in the heart of Mexico City.
Her victory is a major step for Mexico, a country known for its macho culture and home to the world's second-biggest Roman Catholic population.
"It's a historic moment, especially for women," said Arlyn Rivera, a 24-year-old student, as she celebrated Sheinbaum's victory in the Zocalo plaza. "Mexican politics deserves more than what we have had in recent years."
Main opposition rival, Xochitl Galvez, conceded defeat after mustering just 26.6%-28.6% of votes, according to preliminary results.
Sheinbaum, who will take office on Oct. 1, is the first woman to win a general election in North America, comprising the United States, Mexico and Canada.
BUDGET DEFICIT
Sheinbaum has promised to expand the welfare policies that have driven Lopez Obrador's popularity and her triumph, a tricky task while inheriting a hefty budget deficit and low economic growth.
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 crime 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.
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 Donald Trump wins the U.S. presidency 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 drug cartels.
At home, Sheinbaum 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.
She 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."
"There is an expectation that she will continue the policies of Lopez Obrador, but also become her own president at the same time," said Jason Marczak, senior director of the Atlantic Council's Adrienne Arsht Latin America Center.
"I see her administration as being more technocratic than a Lopez Obrador administration, one that is less dependent on the ultimate whims of the president and more about the structure that she has created around her," he said, highlighting Sheinbaum's reputation for efficiency when she was Mexico City mayor.
Political analyst Viri Rios said she thought sexism was behind criticism that Sheinbaum was going to be a puppet.
"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.
