The former bus driver rose through the political ranks with his faithful support of the late President.
More than 20 world leaders are expected to attend the funeral today, but there will be no burial as he will be embalmed.
Thousands flocked to the streets of Caracas to see the coffin of Chavez travel through the city to lie in state until Friday's funeral.
Both sides in an election to choose a successor to Venezuela's late leader Hugo Chavez expressed confidence of victory after Sunday's vote, raising fears that the official result could be contested.
Acting President Nicolas Maduro led all polls before the vote, buoyed by Chavez's blessing before he died from cancer last month and vowing to continue the former president's self-styled socialist revolution.
But Maduro's rival, state governor Henrique Capriles, appeared to close the gap in the last days of the short campaign.
- Read: Fears over Venezuela vote.
Polls have officially closed in Venezuela's presidential election, but some have remained open past the deadline.
- Read: Venezuala voting row.
Following opposition complaints that some people were illegally helping elderly voters cast their ballots, Henrique Capriles urged his followers to report any violations of election laws.
But he also stressed he would respect the outcome of the vote, whatever it might be.
"Today, all Venezuelans are reporters. If you see something irregular, take a picture, air it on social media," Capriles said after voting.
"But let there be no doubt, we will respect the will of the people."
Electoral authorities said voting was going smoothly and that there was no evidence of irregularities.
Given the deep mutual mistrust on both sides, some worry that a close or contested result could spark unrest.
Some 170 international observers were on hand, many from left-leaning political parties across Latin America.
Polls were due to close on Sunday, but voting continued past that in some places to accommodate queues.
The people of Venezuelan voted on whether to honour Hugo Chavez's dying wish for a long time loyalist to continue his self-styled socialist revolution or hand power to a young challenger promising business-friendly changes.
Acting President Nicolas Maduro led opposition rival Henrique Capriles in most polls heading into the vote, buoyed by Chavez's public blessing before he died from cancer last month.
Maduro supporters mobilised voters with pre-dawn bugle calls in the rough barrios of Caracas, where Chavez is revered as a hero of the poor.
"We're going to elect Maduro president because he's following the path set by Chavez," Morelia Roa, a 58-year-old nurse, said after casting her ballot in the same working class Caracas district where Maduro voted.
Lines formed under blistering sunshine at some voting centers, but many were shorter than they were at last October's election, when an ailing Chavez beat Capriles. Then, a record 80 percent of registered voters cast ballots following an aggressive get-out-the-vote campaign by the Chavista camp.
Venezuela opposition candidate Henrique Capriles has alleged via Twitter there is a plan to “change” the country's election result.
Alertamos al país y al mundo la intención de querer cambiar la voluntad expresada por el Pueblo!Hacer RT a este mensaje
Venezuela's opposition leader, Capriles, alleged there was a plan to try and change the results of the South American nation's presidential election.
"We alert the country and the world of the intention to try and change the will expressed by the people," he said in a Twitter message.
Capriles' aides confirmed the tweet was legitimate.
Government officials called it irresponsible.
Venezuelan acting president Nicolas Maduro has said a centuries-old curse would fall on the heads of those who do not vote for him in next week's election to pick a successor to late leader Hugo Chavez.
Maduro's invocation of the "curse of Macarapana" was the latest twist in an increasingly surreal fight between him and opposition leader Henrique Capriles for control of the South American OPEC nation of 29 million people.
"If anyone among the people votes against Nicolas Maduro, he is voting against himself, and the curse of Macarapana is falling on him," said Maduro, referring to the 16th-century Battle of Macarapana when Spanish colonial fighters massacred local Indian forces.
To the cheers of thousands of supporters, acting Venezuelan President Nicolas Maduro officially registered his candidacy today for the upcoming elections.
The 50-year-old arrived to the National Electoral Council driving his own bus to register his candidacy.
"I am going to accomplish his orders (referring to Chavez) with the biggest love that he cultivated in our hearts. I am not Chavez, but I am his son and together with the people, we are Chavez," Maduro said after registering his candidacy.
Both Maduro and opposition leader Henrique Capriles have begun Venezuela's election race with scathing personal attacks on one another.
Maduro, who was sworn in as acting president after Chavez succumbed to cancer last week, is seen as the favourite to win the April 14 election, bolstered by an oil-financed state apparatus and a wave of public sympathy over Chavez's death.
Venezuelan opposition leader Henrique Capriles said he will challenge the late Hugo Chavez's preferred successor for the presidency of the South American OPEC nation next month, setting the stage for a bitter campaign.
Capriles, a 40-year-old state governor, will face election favourite and acting President Nicolas Maduro. The pair have until Monday to register their candidacies for the vote on April 14th.
The election will decide whether Chavez's self-styled socialist and nationalist revolution will live on in the country with the world's largest proven oil reserves.
Opposition leader Henrique Capriles will run for president in Venezuela's April election and is expected to formally announce the decision later today, two sources in his camp said.
"There's a lot of negativity around, it's going to be tough, but we're going to do it", one of the sources told Reuters.
"Henrique's made his decision. He's not backing down."
Venezuela's centrist opposition leader, Henrique Capriles, said he was "evaluating" the election date ruling and has thanked the coalition for proposing his candidacy.