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