Mr Chavez had been seriously ill with cancer for more than a year, undergoing several operations in Cuba, and had not been seen in public for several months.
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 held within 30 days, Mr Jaua added.
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 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 4:25 pm,” he added.
Earlier, he said the Venezuelan leader had a severe respiratory infection and had entered “his most difficult hours”.
He 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.
Struggling to hold back tears, Mr Maduro called on the nation to close ranks after their leader’s demise.
He said the government had deployed the armed forces and police nationwide “to accompany and protect our people and guarantee the peace”.
Earlier, he said he had expelled two US diplomats from the country for spying on Venezuela’s military.
A statement by the military 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.
Mr Jaua 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.
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.
In Argentina, President Cristina Fernandez de Kirchner suspended all activities after the death was announced.
Both she and her late husband, Nestor Kirchner, were close friends of the firebrand Venezuelan leader.
In Peru, Congress held a minute of silence in his honour. Bolivia’s President Evo Morales said he was leaving immediately for Caracas.
The governments of Chile and Ecuador also released official notes of condolence to Venezuela.
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.
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.
Mr Chavez was renowned for his flamboyant public speaking style, which he put to use in his weekly live TV programme, Alo Presidente (Hello President), in which he talked about his political ideas, interviews guests and sings and dances.
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 should the need arise.
Mr Chavez remained out of public view, finally returning to Venezuela in February.
Hugo Chavez was born on 28 July 1954 in Sabaneta, Barinas state, the son of schoolteachers. He went on to study at Venezuela’s military academy and served in the armed forces for a number of years.
After founding a revolutionary unit within the military, he led an unsuccessful coup against President Carlos Andres Perez in 1992. This launched him onto the political scene but also earned him two years in prison.
After his release, Mr Chavez established the Fifth Republic Movement, which would lead him to power in 1998. Campaigning against the establishment and as a champion of the poor, he won 56% of the vote.
Mr Chavez then won a series of elections and referendums, including one on changing the constitution to allow unlimited presidential terms. He established close ties to the Cuban government of Fidel Castro.
Opponents of Mr Chavez’s government accused the president of becoming increasingly autocratic. In 2002 a group of military officers launched a short-lived coup that saw him removed from office for two days.
He survived the episode and went on to victory in the 2006 election. He implemented universal health and education programmes, but rising prices and shortages of basic goods meant life remained hard for some.
In May 2012, Mr Chavez said he had recovered from an unspecified cancer, but in December underwent further surgery and named his vice-president, Nicolas Maduro, as his choice as successor.