Foreign Minister Elias Jose Jaua Milano declared seven days of mourning and said Mr Chavez's body would lie in state until his funeral on Friday.
Vice-President Nicolas Maduro would assume the presidency until an election was called within 30 days, he added.
"It is the mandate that Comandante President Hugo Chavez gave us," Mr Jaua told state television, adding that Mr Maduro would also be the candidate of the governing United Socialist Party (PSUV).
It was not immediately clear when the election would take place.
Mr Chavez's illness prevented him from taking the oath of office after he was re-elected for a third term in October and the President of the National Assembly, Diosdado Cabello, had been expected by some to take over as interim president in the event of his death.
However, he was not among the political and military leaders who flanked the vice-president when he announced Mr Chavez's death.
In Tuesday's televised address, a tearful Mr Maduro said the president had passed away "after battling a tough illness for nearly two years".
"We have received the toughest and tragic information that... Comandante President Hugo Chavez died today at 16:25 (20:55 GMT)," he added.
Mr Maduro called on the nation to close ranks after its leader's demise.
"Let there be no weakness, no violence. Let there be no hate. In our hearts there should only be one sentiment: Love."
But he revealed that the government had deployed the armed forces and police nationwide "to accompany and protect our people and guarantee the peace".
The vice-president also spoke of a plot against Venezuela, saying he had no doubt that Mr Chavez's cancer, first diagnosed in 2011, had been induced by foul play by Venezuela's enemies - the US promptly rejected the accusations as "absurd".
He said a scientific commission could one day investigate whether Mr Chavez's illness was brought about by what he called an enemy attack.
Two US diplomats had been expelled from the country for spying on Venezuela's military, he added.
A statement by the military issued after Mr Chavez's death said it would protect the sovereignty, integrity and security of the country. It would remain loyal to the vice-president and to parliament, it added, urging people to remain calm.
Mr Jaua said a procession would carry Mr Chavez's body to the Military Academy in Caracas on Wednesday, where it will lie in state until Friday to allow his supporters to pay their respects.
He added that the official funeral attended by foreign heads of state would take place at 10:00 local time (14:30 GMT) on Friday, and called on Mr Chavez's supporters to wear clothes in the three colours of the Venezuelan flag in his honour.
Hundreds of Chavez supporters appeared in front of the hospital where he died, shouting:"We are all Chavez!" and "Chavez lives!"
One of them, Francis Izquierdo, told Agence France-Presse: "He was a man who taught us to love our fatherland. The comandante is physically gone but he remains in our hearts and we must continue building the fatherland."
Opposition leader Henrique Capriles, whom Mr Chavez defeated in October's election, called on the government to "act in strict accordance with its constitutional duties".
But he also told Venezuelans wondering what might happen: "They should have no fear and feel no anxiety, because between us all we are going to guarantee peace that this dear fatherland deserves."
The opposition has yet to confirm who will be its official candidate for the presidential election, but Mr Capriles is widely expected to be chosen to stand against the vice-president.
The BBC's Irene Caselli, in Caracas, says Mr Maduro will probably win, but the question remains whether he will be able to lead Venezuela following the loss of its iconic president.
The US described the death as a "challenging time", reaffirming what it described as its support for the Venezuelan people and its interest in developing a constructive relationship with Caracas.
"As Venezuela begins a new chapter in its history, the United States remains committed to policies that promote democratic principles, the rule of law, and respect for human rights," said a statement from the White House.
Russia's permanent representative to the UN, Vitaly Churkin, said Mr Chavez had been a great politician, for his country, for Latin America and the world.
The government of Cuba declared three days of national mourning. In a statement read out on state television, it said Mr Chavez had "stood by Fidel [Castro] like a true son", referring to Cuba's former president, who stepped down in 2006 due to ill-health.
In Argentina, President Cristina Fernandez de Kirchner, a close friend, suspended all activities after the death was announced.
Peru's Congress held a minute of silence in his honour while Bolivia's President Evo Morales said he was leaving immediately for Caracas.
The Ecuadorian government said it felt the loss as its own, and hoped its neighbours could carry on Mr Chavez's revolution.
Analysts say Mr Chavez's death could alter the political balance in Latin America - dealing a blow to leftist states while favouring more centrist countries.
There could also be an economic impact given that Venezuela sells oil at below market prices to some neighbouring countries, especially in the Caribbean.
UK Foreign Minister William Hague said he was "saddened" to learn of the death, saying Mr Chavez had left a "lasting impression" on Venezuela.
One of the most visible, vocal and controversial leaders in Latin America, Hugo Chavez won the presidency in 1998 and had most recently won another six-year presidential term in October 2012.
His government has implemented a number of "missions" or social programmes, including education and health services for all. But poverty and unemployment are still widespread, despite the country's oil wealth.
Last May, the former army paratrooper said he had recovered from an unspecified cancer, after undergoing surgery and chemotherapy in 2011 and a further operation in February 2012.
However, in December, he announced he needed further cancer surgery in Cuba, and named Mr Maduro as his preferred successor. Mr Chavez returned to Venezuela in February, but was confined to hospital.