The National Electoral Council said Maduro won 50.7 percent of the votes, compared to 49.1 percent for his young rival, Miranda state Governor Henrique Capriles. It said more than 99 percent of the votes had been counted and that the result was "irreversible."
Chavez, who ruled for 14 years, anointed Maduro as his political heir in his last speech to the country before succumbing to cancer on March 5.
That gave his former vice president and foreign minister a huge advantage but Capriles narrowed the gap in the final days of the campaign and the result was much closer than many had expected.
"I'm here to assume my responsibility with courage ... The fight continues!" Maduro, 50, told a victory rally.
There was no immediate response from Capriles, who earlier on Sunday alleged that there was a plan to try to change the result of the election.
Capriles, 40, had argued that voters were tired of divisive Chavez-era politics, and vowed to tackle daily worries such as violent crime, high inflation and creaking utilities.
But in Venezuela's first presidential election without Chavez for two decades, the ruling Socialist Party's powerful get-out-the-vote machinery swung into action behind Maduro.
Chavez's death, at 58, had cemented his already cult-like status among supporters, who adored his down-to-earth style, humble beginnings, aggressive "anti-imperialist" rhetoric, and channeling of oil revenue into social welfare projects.
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