Results released by the Elections Commission early Monday morning showed Solih had secured 58.3 percent of the popular vote.
Celebrations broke out across the tropical archipelago with opposition supporters carrying yellow flags of Solih’s Maldivian Democratic Party (MDP) and dancing on the streets. There was no response from Yameen after results were announced.
Solih had the backing of a united opposition trying to oust Yameen but struggled for visibility with the electorate, with local media fearful of falling afoul of heavy-handed decrees and reporting restrictions.
There were also no other candidates at Sunday’s election held with all key dissidents either in jail or exile.
Earlier in the night Solih had called on Yameen to concede defeat once the tally showed he had an unassailable lead.
“I call on Yameen to respect the will of the people and bring about a peaceful, smooth transfer of power,” he said on television.
He also urged the incumbent to immediately release scores of political prisoners.
Yameen, who was widely tipped to retain power, had jailed or forced into exile almost all of his main rivals.
Before polls opened, police raided the campaign headquarters of the opposition Maldivian Democratic Party (MDP) and searched the building for several hours in a bid to stop what they called “illegal activities”. There were no arrests.
Mohamed Nasheed, the head of the MDP, said the vote would “bring the country back to the democratic path”.
Yameen would have no option but to concede defeat, said Nasheed, who was elected president of a newly-democratic Maldives in 2008 but currently lives in exile.