In runoff voting Saturday, Yameen received 51.3 percent of the vote, while former president Mohamed Nasheed received 48.6 percent, the BBC reported.
Some of 98 percent of the ballots have been counted, the Election Commission said.
Nasheed received 47 percent of the votes in last Saturday's election, forcing the second round of voting, Voice of America reported. Yameen won 30 percent of the votes.
Nasheed was forced to resign in 2012.
The runoff had been scheduled for the Sunday after the initial balloting, but was postponed after other candidates petitioned the country's high court for a delay.
Nasheed won an earlier election in September, but the Supreme Court threw out the results. A second election scheduled for October was canceled.
Elections Commission official Aishath Reema said many voters were already in line when polling stations opened Saturday, the BBC reported.
Yameen's half-brother, Maumoon Abdul Gayoom, was president of the Maldives from 1978 to 2008, when he was defeated for re-election by Nasheed.
The man who replaced Nasheed after his resignation, Mohamed Waheed, left the country Thursday to accompany his wife to a medical appointment in Hong Kong.
Waheed's term expired last weekend and he did not seek re-election.
The Maldives are a chain of 26 atolls southwest of the southern tip of India.