Election officials said Rajapakse, who is being challenged by his former army chief Sarath Fonseka, had won over 60 percent of the vote with about one-tenth of the ballots counted.
The winner was set to be announced around noon (0630 GMT) on Wednesday by Election Commissioner Dayananda Dissanayake.
The island nation's presidential vote Tuesday was the first since Rajapakse and Fonseka engineered the final defeat of Tamil Tiger separatists last year after three decades of civil war.
The campaign's vitriolic nature, coupled with warnings from the opposition of protests, fraud and state-backed coups, had raised fears that the loser might reject the result and foment new unrest instead of a peace dividend.
But Media Minister Anura Priyadharshana Yapa said Rajapakse, who like Fonseka is a member of Sri Lanka's dominant Sinhalese community, was "heading for a historic victory".
The first official results showed Rajapakse getting 723,362 votes against 460,725 for Fonseka. An estimated 9