His rivals conceded defeat when results tabulated by local media from official results showed him taking slightly more than half of the vote, much higher than predicted.
Electoral officials were due to release results on Monday and, if they confirm that Morales won more than 50% of the votes, he avoids facing a congressional choice between him and the right-wing Jorge "Tuto" Quiroga, who came a distant second.
Amid chants of "Evo president! Evo president!" by hundreds of supporters at his campaign headquarters in Cochabamba on Sunday night, Morales said: "Beginning tomorrow, Bolivia's new history really begins: A history where we will seek equality, justice, equity, peace and social justice."
Landlocked Bolivia, South America's poorest and least-stable country, has seen two presidents in three years toppled by large-scale demonstrations led by out-of-work miners, disenfranchised Indians and coca-leaf growers.
"Beginning tomorrow, Bolivia's new history really begins: A history where we will seek equality, justice, equity, peace and social justice"
Bolivian president elect
The new government will face conflicting demands from Indian groups, who want the constitution rewritten to enshrine Indian rights, and from the country's wealthy eastern provinces, where an elite wants greater power for regional governments.
Nationalising gas industry
Morales has pledged to nationalise the natural gas industry - Bolivia has South America's second-largest reserves of the fuel - tuning in to popular disillusionment with free-market economic policies that many say did little to help the poor.
Morales, who admires the drive for regional co-operation to counter US influence by Hugo Chavez, the Venezuelan president, also tapped into frustrations of the Quechua, Aymara and other Indian groups that are a majority in the Andean country.
His most fervent support comes from Indians who see one of their own reversing what most see as more than 500 years of discrimination under leaders of European heritage, beginning with slavery in Spanish colonial silver mines.
Bolivian Indians strongly support
Morales, one of their own
A high-school dropout who herded llamas as a boy, Morales has vowed to roll back a US-backed eradication programme of coca, the main ingredient in cocaine but also prized by Indians for traditional medicinal uses.
Washington considers Morales, who first rose to power as the leader of the country's coca farmers, an enemy in its anti-drug fight in Bolivia, the third-biggest cocaine producer after Colombia and Peru.
Morales has described himself as Washington's "nightmare".
A Morales presidency will add Bolivia to a drift to the left across the region that has seen leftist presidents come to power in Argentina, Brazil, Uruguay and Venezuela.