He also urged the incumbent to immediately release scores of political prisoners.
Hours ahead of the voting on Sunday, police searched Mr Solih's campaign office to investigate "acts of bribery", a move described by the opposition as yet another effort to influence the outcome of the polls.
Ibrahim Mohamed Solih won the elections with 134,616 votes.
But unlike other reformers of his generation, Solih was never sidelined by a prison sentence or political exile, a fact that propelled him into the role of the opposition party's standard-bearer. "People want justice and stability and we will ensure accountability", he added.
The European Union and United States have voiced concerns about the election and have threatened to impose targeted sanctions if the democratic situation does not improve.
"Although the Election Commission has not as yet announced the final results, we congratulate Mr. Solih on his victory and look forward to working closely with him and the people of the Maldives in pursuing the elevation of relations between the Maldives and Sri Lanka to greater heights". The voter turnout was over 88 per cent out of the 262,000-strong electorate.
While Nasheed and Gayoom have had close relationships with China in the past during their presidency, the Indian view is that as long as its interests are not impacted, Male is free to develop its bilateral ties with third countries.
Only a handful of foreign media were allowed in to cover the poll.
Since coming to power in a contested election in 2013, Yameen has been criticised for jailing opponents and restricting election observers and the media, and there had been fears that Sunday's election would an unfair contest.
Solih campaigned door to door, speaking at rallies about human rights and the rule of law, a message that resonated with voters who saw signs the Maldives was slipping back to autocratic rule, just a decade after achieving democracy.
In February, Yameen declared a state of emergency, suspended the constitution and ordered troops to storm the Supreme Court and arrest judges after they had ordered the release and retrial of those jailed after politically-motivated trials.
One of the most senior politicians in the Maldives, and has for years been calling for democratic reform.
Beijing loaned Yameen's government hundreds of millions of dollars for infrastructure projects like the new "China-Maldives Friendship Bridge", which opened in August.
Signalling the impact of the result on India, which has been at loggerheads with the Yameen government over a number of issues, the Ministry of External Affairs "heartily" congratulated Solih and hoped that the "Election Commission will officially confirm the result at the earliest".