CLAUDIA SHEINBAUM has been elected as Mexico's first woman president in an historic landslide win.

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 the election.

That gives her a lead of about 30 percentage points over her main rival, XÓCHITL GÁLVEZ.

SHEINBAUM will replace her mentor, outgoing President ANDRÉS MANUEL LÓPEZ OBRADOR, on October 1.