Zelaya, the Liberal Party candidate, said: "Reason and love have triumphed over fear. Honduras needs fundamental change in its democratic system that can only be wrought by citizen power."
Zelaya defeated Lobo Sosa, of the governing National Party, who garnered 44.3% of the vote, the survey found.
The exit poll of 120,000 voters was conducted by General Engineering and published by local media.
Early ballot returns on Sunday showed similar results, with 50.8% of votes for Zelaya and 45.2% for Lobo Sosa, the country's national election institute announced.
The percentage of votes counted was not released, and officials said no further information would be available until Monday at the earliest.
Vowing to eliminate widespread government corruption, Zelaya had clashed on law-enforcement issues with Lobo Sosa, who has promised to wipe out violent crime with the help of the death penalty.
Zelaya flew from his home province of Olancho, where he had voted earlier on Sunday, to campaign headquarters in Tegucigalpa to declare himself the winner.
Zelaya supporters broke into
His supporters broke into raucous celebration at his campaign headquarters with music and dancing and flooded into the streets of the capital waving the Liberal Party's flag, celebrating what they called a certain victory.
"Honduras has today a new light of hope," Zelaya said at a news conference. "Now comes an era of transparency and justice."
But in an interview with local media, Lobo Sosa said: "We have results that don't coincide with those of the Liberal Party ... It is a close race and it will be a long night of counting votes."
The country's nearly 4 million voters also cast ballots for a vice-president, 128 congressional representatives, 298 mayors and 2000 city councillors.
Sunday's vote is the seventh consecutive democratic election of this Central American nation since 1981, when it abandoned more than two decades of military rule.
Governing party candidate Lobo
Sosa said it remained close
Sunday's balloting took place under the eyes of more than 16,000 soldiers and police officers, as well as 6000 local observers and 114 election monitors from 14 countries.
There were no serious irregularities or incidents reported.
Zelaya, a former congressman and bank director, says the shortest road to prosperity for a country with a 70% poverty rate is to eliminate corruption, which he claims is rife in the National Party-ruled government and the private sector.
He has proposed a transparency law and a civil assembly to monitor the government as well as promised to support life imprisonment for hard-core criminals.
Honduran law does not allow life imprisonment.
Lobo Sosa, as congressional president, helped current President Ricardo Maduro push through laws to criminalise gang membership. Maduro is not allowed by law to run for re-election.
Both Lobo Sosa and Zelaya are wealthy agricultural landowners who support a free-trade agreement with the