Almost 90 percent of the 262,000 electorate turned out to vote, with some waiting in line for more than five hours as officials encountered technical glitches.
Independent election watchdog Transparency Maldives tweeted that Solih has won "by a decisive margin".
Joint presidential candidate for an opposition alliance - which includes the MDP, the Jumhooree Party and the Adhaalath Party.
In a victory speech in Maldives' capital Male, Solih called it "a moment of happiness, hope and history".
Hundreds of people gathered outside the main opposition campaign center in Male in a jubilant mood, chanting "Ibu, Ibu, Ibu" and calling on Yameen to concede defeat.
Voting closed at 1900 hours (1400 GMT), after the Indian Ocean nation's Election Commission extended voting by three hours because of long queues at polling stations.
24 killed, dozens wounded in 'terrorist' attack in Iran
Iran will be scrambling to determine the motives for the Saturday's high-profile attack as it faces growing US pressure. Iran has also alleged that the gunmen had links to its bitter foe Israel .
Lying southwest of India, and stretching across maritime routes that are crucial to China, the Maldives has been caught up in recent years in Beijing's growing global ambitions, which the United States and its allies have struggled to contain. The governments of both countries reject that assessment.
Maldivian president Yameen Abdul Gayoom, right, casts his vote at a polling station during presidential election day in Male, Maldives, Sunday, Sept. 23, 2018.
A warrant for the raid obtained by The Associated Press cited police intelligence of possible vote-buying at the campaign office.
Rohana Hettiarachchi, a member of the Asian Network for Free Elections, which was named as an election monitor, said his organization could not take part.
The European Union and United States had earlier voiced concerns about the election, with both threatening to impose targeted sanctions if the democratic situation did not improve.
The European Union said on Friday that it was not sending election observers because the Maldives had failed to meet the basic conditions for monitoring.
More possible victims of California doctor found
Cerissa Laura Riley , 31, of Brea, was also charged, with a sentencing enhancement of knowingly vicariously armed with firearm. Lauren Hayden said she sensed something was wrong when she went on a date with prominent doctor Grant Robicheaux a year ago .
Before the election there were warnings that Yameen could try to hold on to power at all costs.
A crackdown saw former president Maumoon Abdul Gayoom - Yameen's half-brother - jailed along with the Chief Justice and another Supreme Court justice amid accusations of an imminent coup. Around 10,000 people attended, about twice as many as at the governing party's rallies, though in the past the government has used force to stifle protests and dismissed dissenters as terrorists.
British Ambassador James Dauris wrote on Twitter that it was "easy to understand why so many people are concerned about what might happen on election day". "President Yameen was not given a mandate to trample all over Maldivian democracy and our Constitution, but that is what he has done these past five years".
Under Mr Yameen, the Maldives has also welcomed Chinese money for major projects and signed a free trade agreement.
The Yameen administration was widely criticised for systematically suppressing opposition, rolling back democratic freedoms, jailing rivals and controlling courts. Critics say Mr. Yameen's rule was slanted towards authoritarianism.
Still, Fiasal said, the result was surprising because "no one thought that Yameen would lose like this".
Android Pie-Based Oxygen OS 9.0 Now Available For OnePlus 6
This update also rolls with Gaming mode 3.0, which adds notifications for 3rd-party calls as well as text notification mode. It also gets Adaptive Battery feature that monitors what apps are using most battery, and prevent them from draining it.