Claudia Sheinbaum has been elected as Mexico's first woman president in an historic landslide win, BBC reported.

Mexico's official electoral authority said preliminary results showed the 61-year-old former mayor of Mexico City winning between 58 per cent and 60 per cent of the vote in Sunday's election.

Sheinbaum will replace her mentor, outgoing President Andrés Manuel López Obrador, on 1 October.

Sheinbaum, a former energy scientist, has promised continuity, saying that she will continue to build on the "advances" made by 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."

Sheinbaum also thanked her rival, Xóchitl Gálvez, who has conceded victory.

bd-pratidin/GR