President Gayoom won the first round earlier this month, but failed to secure the 50% needed for outright victory over Mr Nasheed.
With almost all the votes counted, Mr Nasheed, a former political prisoner was reported to have won 54% compared to Mr Gayoom's 46%.
Speaking to the BBC, Mr Nasheed, also known as Anni, claimed victory, and said the people of the Maldives were embracing the future.
He said he had spoken to Mr Gayoom and the two men would meet later in the day.
The election was the culmination of reforms in the islands in the Indian Ocean that followed street pro-democracy protests and international pressure.
President Gayoom, 71, has ruled the Maldives uncontested since 1978, elected back into office six times by referendums.
The BBC's Roland Buerk in the capital Male said Mr Gayoom's supporters had credited him with overseeing an economic expansion fuelled by tourism.
But Mr Gayoom's critics say he was a dictator who ruled like a sultan of old, says our correspondent.
Courtesy: BBC News
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