Yameen secured 51.3 per cent of the popular vote compared to 48.6 per cent for ex-president Nasheed in Saturday's run-off vote after a contest wracked by lengthy delays that were viewed as politically motivated, elections commission results showed.

Despite the acrimonious campaign, Nasheed conceded defeat and said he would not challenge the results of an election monitored by international observers.

"I graciously accept defeat," Nasheed told reporters on the main capital island of Male in a late night address.

"We lost by a very small margin. Democracy is a process. It is up to us to make it work."

He added: "The MDP (Nasheed's Maldives Democratic Party) has always asked for a government elected by the people. Today is a happy day for the Maldives — we now have an elected government."

The election commission said that an inauguration ceremony would take place on Sunday and a special session of parliament had also been organised.

Nasheed's concession will be a relief to the country's lifeblood tourist industry which had feared that an already lengthy political crisis could go on even longer.

After an annulled election result and two cancelled polls, foreign diplomats had increasingly come to view the delays as politically inspired. The European Union had warned of "appropriate measures" if Saturday's election did not go ahead as scheduled.

Opposition leader Nasheed, a former pro-democracy campaigner and climate change activist who won the first free polls in 2008, had been the frontrunner 21 months after he resigned under pressure from demonstrators and mutinous police officers.

However, his main opponents united after his first round victory on November 9 and mounted a formidable challenge, leading to Yameen's victory.

Yameen is the half-brother of former autocrat Maumoon Abdul Gayoom who ruled the archipelago famed for its coral-fringed islands for 30 years, before the nation embraced democracy.

The islands' electorate is a mere 239,000 people in a country of 350,000 Sunni Muslims.

After casting his vote, Yameen said he had no complaints about the electoral process.

"I will accept the results no matter what the outcome," he told reporters.

Nasheed, a one-time political prisoner, won a first vote on September 7 with 45 per cent.

But the result was annulled by the supreme court which upheld a complaint about voter list irregularities.

After another attempt to hold the poll was blocked, a re-run of the first round took place on November 9 which Nasheed won by a larger margin — nearly 47 per cent — but still not enough for an outright victory.

A run-off election announced for the day after by the independent elections commission was again cancelled by the supreme court, which is dominated by judges appointed during Gayoom's three-decade rule.