Exit polls showed Correa, who has pledged to radically reform Ecuadorean politics, has a wide lead over Noboa.
Correa, a US-trained economist, told supporters that we "accept this victory with dignity and humility".
Pollster CEDATOS-Gallup said Correa, an ally of Hugo Chavez, the Venezuelan president, received 56.8 per cent of the votes compared to Noboa, who gained 43.2 per cent.
Market, a second pollster, gave Correa 58 per cent to 42 per cent for Noboa.
At a news conference in Quito, Correa said: "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."
However, Noboa immediately rejected Sunday's exit poll results, saying he would wait for the official count to end.
He said in a television interview: "I know in my interior that I won. The electoral tribunal will give the official figure once it has finished the vote count."
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.
Correa's election would add another member to South America's grouping of left-leaning nations, which already includes Venezuela, Chile, Bolivia, Brazil, Argentina and Uruguay.
Noboa, a billionaire, had run an old-fashioned populist campaign, crisscrossing Ecuador, from its Pacific coast to the Andes and eastward to the Amazon jungle, handing out computers, medicine and money.
He said he was willing to accept a clean defeat, but "if it is fraudulent, we will never accept it".