Mexico’s official electoral authority said preliminary results showed the 61-year-old former mayor of Mexico City winning between 58% and 60% of the vote in Sunday’s election.
That gives her a lead of about 30 percentage points over her main rival, businesswoman Xóchitl Gálvez.
Ms Sheinbaum will replace her mentor, outgoing President Andrés Manuel López Obrador, on 1 October.
Ms Sheinbaum, a former energy scientist, has promised continuity, saying that she will continue to build on the “advances” made by Mr López Obrador, further building on the welfare programmes which have made the outgoing president very popular.
But in her victory speech she also highlighted what has set this Mexican election apart from previous ones. She told cheering voters: “For the first time in the 200 years of the [Mexican] Republic, I will become the first woman president of Mexico.”
She said, it was an achievement not just for her but for all women.
“I’ve said it from the start, this is not just about me getting [to the top office], it’s about all of us getting here.”
She added: “I won’t fail you.”
Ms Sheinbaum also thanked her rival, Xóchitl Gálvez, who has conceded victory.
Prior to running for president, Ms Sheinbaum was mayor of Mexico City, one of the most influential political positions in the country and one that is seen as paving the way for the presidency.
Ms Sheinbaum, whose Jewish maternal grandparents immigrated to Mexico from Bulgaria fleeing the Nazis, had an illustrious career as a scientist before delving into politics. Her paternal grandparents hailed from Lithuania.
Both of her parents were scientists and Ms Sheinbaum studied physics before going on to receive a doctorate in energy engineering.
She spent years at a renowned research lab in California studying Mexican energy consumption patterns and became an expert on climate change.
That experience and her student activism eventually earned her the position of secretary of the environment for Mexico City at the time when Andrés Manuel López Obrador was mayor of the capital.
In 2018 she became the first female mayor of Mexico City, a post she held until 2023, when she stepped down to run for president.
