The result marks a return to the left for Bolivia from the present conservative caretaker government that stepped in after leader Evo Morales was ousted last year.
Polls showed Bolivia's socialist candidate Luis Arce has 52.4 percent of valid votes, more than 20 percentage points above second-place centrist rival Carlos Mesa.
Evo Morales, country's first indigenous president, says his opposition rivals "will go down in history as racists and coup plotters," day after he resigned and fled to central Chapare region. Meanwhile, US "applauds" Bolivia's army for his ouster.
The election result means President Evo Morales has won a fourth successive term despite the constitution he promulgated in 2009 limiting presidents to two mandates.
Bolivian President Evo Morales led Sunday's election but did not have enough votes to avoid a potentially risky runoff with rival Carlos Mesa in December, a preliminary count of nearly 84 percent of official results by the electoral board showed.
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