However, opposition candidate Henrique Capriles has refused to accept the result and demanded a full recount.
Mr Maduro's close victory followed a campaign in which the winner promised to carry on Mr Chavez's self-styled socialist revolution.
Mr Capriles's main message was that Mr Chavez put the country with the world's largest oil reserves on the road to ruin.
Mr Maduro, who had been acting president since Mr Chavez's death on 5 March, held a double-digit advantage in opinion polls just two weeks ago.
However, electoral officials said he got 50.7% of the votes to 49.1% for Mr Capriles with nearly all ballots counted.
The margin was about 234,935 votes. Turnout was 78%, which was down from just over 80% in the October election that Mr Chavez won by a nearly 11-point margin.
In a victory speech, Mr Maduro told a crowd outside the presidential palace that his victory was further proof that Mr Chavez "continues to be invincible".
Mr Capriles reacted angrily to the result, saying: "It is the government that has been defeated."
He said his campaign came up with "a result that is different from the results announced today".
"The biggest loser today is you," Mr Capriles said, directly addressing Mr Maduro through the camera. "The people don't love you."
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