The national electoral commission has not yet announced official results.
But Mr Solih has said he won Sunday's vote by a 16% margin, with 92% of the votes counted.
He has already called on President Abdulla Yameen to "accept the will of the people".
"The message is loud and clear. The people of Maldives want change, peace and justice," Mr Solih, widely known as Ibu, told reporters in the capital, Male.
President Yameen, who had been widely expected to win another term in office, has not yet commented publicly.
Mr Yameen's government stands accused of crushing dissent and observers had believed the election was rigged in his favour.
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