The ex-Mexico City mayor, known by his initials Amlo, is projected to win about 53%. His rivals have conceded in a crushing defeat for the main parties.
Mr López Obrador's key pledge has been to tackle the "evil" of corruption.
He has also been highly critical of President Donald Trump and ties with the US will now be closely watched.
Relations with Washington have been hugely strained, with Mr Trump strongly criticising Mexico over trade and migration. Mr Trump has sent a tweet of congratulations.