The National Electoral Council backed the slender victory of Nicolas Maduro, the acting president, despite protests from opposition candidate Henrique Capriles.
The official count indicates Nicolas Maduro won 50.7% of votes to Henrique Capriles’ 49.1%.
Following the announcement, clashes broke out between protesters and police in the capital Caracas.
Police fired tear gas at hundreds of students demonstrating in one part of the city, while elsewhere opposition supporters took to their balconies and the streets to bang pots and pans in protest.
Henrique Capriles had earlier urged national protests and a march on the electoral offices in the capital in the event that Nicolas Maduro was declared the winner.
He called on the National Electoral Council not to confirm the election result, citing voting irregularities, and demanded a recount.
Henrique Capriles said he regarded the election of Nicolas Maduro as “illegitimate”.
The poll was called after President Hugo Chavez died of cancer last month.
Nicolas Maduro is a former bus driver who rose to become Hugo Chavez’s vice-president and heir apparent.
Henrique Capriles said there were more than 3,200 “incidents” from Sunday’s poll that needed to be examined.
“All we’re asking is that our rights be respected, that the will of the people be respected, and that every single vote be counted, every little piece of paper,” he told a news conference broadcast on national television.
But while it has agreed to an audit of the electronic counting system, the government is rejecting calls that the ballot boxes be opened for a manual recount.
Monday saw opposition students briefly invade a hotel where international election observers are staying, demanding to know why the vote had been declared free and fair.
Russian President Vladimir Putin and Cuban leader Raul Castro were among the first heads of state to congratulate Nicolas Maduro on his win.
But the US has called for an audit of the results.
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