His top rivals already conceded defeat Sunday night, based on exit polls.
Morales would become the first president in Bolivian history from the country's Indio ethnic majority, who make up 70 per cent of the population.
With 33 per cent of the vote counted late Monday, Morales had 48 per cent. Centre-right politician Jorge Quiroga was at 35 per cent, and industrialist Samuel Doria Medina was at 9 per cent, according to Bolivia's central election commission.
Exit polls after Sunday's voting put Morales, 46, the socialist leader of Bolivia's indigenous coca farmers, at 51 per cent, with Quiroga at 34 per cent.
If Morales falls short of 50 per cent in final results, Bolivia's constitution requires parliament to choose between the top two finishers.
He campaigned on a left-wing platform to legalize coca, nationalize Bolivia's oil industry and redistribute wealth. He has also embraced Venezuelan President Hugo Chavez, joining the left-wing populist in opposing the U.S.-led free trade agenda in the western hemisphere.
Sunday's election also saw voting for the bicameral National Congress and provincial governments. Morales' Movement Toward Socialism (MAS) was unlikely to win a majority in parliament, but he was expected to still win a parliamentary vote to decide the presidency, if necessary.
Morales supported celebrated late Sunday and Monday throughout Bolivia.
Final vote totals were not expected before Tuesday.
About 200 international election monitors were in Bolivia Sunday, including a large delegation from the Organization of American States (OAS). No serious violence or procedural problems have been reported.
The inauguration of a new president is scheduled for January 22.
