Narciza Subia, one of seven Supreme Electoral Tribunal judges, said on Tuesday: "Rafael Correa is the new president of Ecuador. The trend is not going to change."
Correa, a friend of Hugo Chavez, the Venezuelan president, joins a tide of left-wing leaders elected to office in Latin America.
The election result follows the most recent comeback earlier this month in Nicaragua of the Cold war enemy of the US, Daniel Ortega.
Left-leaning leaders, some more moderate than others, govern in Argentina, Bolivia, Brazil, Chile, Cuba, Uruguay, as well as Nicaragua and Venezuela, where Chavez looks certain to win re-election on Sunday after eight years in office.
Victory speech
Correa, a US-trained economist, had earlier announced victory and told a news conference in Quito: "Thank God, we have triumphed. We are just instruments of the power of the people. This is a clear message that the people want change."
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"We are just instruments of the power of the people. This is a clear message that the people want change"
Rafael Correa
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He said he would keep his promise to carry out widespread reforms which include re-negotiating debt agreements, opposing a US free-trade pact and re-writing the constitution.
He later told reporters in his tropical home city Guayaquil: "The people have given us a clear mandate, with the second-largest margin in the last 30 years of democracy.
"We want a deep political reform."
Correa won a place in Sunday's run-off by pledging a "citizens' revolution" against the discredited country's political system.
Ecuadoreans have driven the last three elected presidents from power, and Correa appealed to voters as a fresh face in a field of established politicians.
He has pledged to construct 100,000 low-cost homes and copied Noboa's promise to double to $36 a "poverty bonus" that 1.2 million poor Ecuadoreans receive each month.