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.
Vice-President Nicolas Maduro made the announcement on Tuesday, flanked by political and military leaders.
The government said Mr Chavez’s body would lie in state until Friday, when his funeral would be held. Seven days of mourning were also declared.
According to the constitution, the President of the National Assembly, Diosdado Cabello, will take over as interim president until an election can be held.
In Tuesday evening’s emotional address, a tearful Vice-President Maduro said Mr Chavez 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,” Mr Maduro said.
Earlier, he said the Venezuelan leader had a severe respiratory infection and had entered “his most difficult hours”.
Will GrantBBC News, Central America correspondent
The death of Hugo Chavez, the vanguard of what he called “21st Century Socialism”, sends ripples not just through the Venezuelan people, but across Latin America and beyond.
In particular, the impact of his loss will be felt most keenly in Cuba, Bolivia and Ecuador, his closest allies in the region.
The updates on his health in recent days had seemingly been aimed at preparing the Venezuelan people for the worst, with each bulletin more serious than the last.
Now Mr Chavez will take on iconic status as his revolution looks for a route forward without him, the man it was designed by and constructed around.
But his millions of followers in Venezuela will take some comfort from the fact that it wasn’t the failed coup in 2002, nor the repeated efforts at the ballot box, but rather ill health – or for many of his devotees, the hand of God – that took Mr Chavez away from them.
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.
Later, Foreign Minister Elias Jose Jaua Milano announced that the government had declared seven days of mourning.
A procession will 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.
Timeline: Hugo Chavez
- 1954: Born 28 July in Sabaneta, Barinas state, the son of schoolteachers
- 1975: Graduated from Venezuelan Academy of Military Sciences
- 1977: Becomes involved in revolutionary movements within the armed forces
- 1981: Returns to the military academy as a teacher
- 1992: Leads doomed attempt to overthrow government of President Carlos Andres Perez, jailed for two years
- 1994: Relaunches his party as the Movement of the Fifth Republic
- 1999: Takes office after winning 1998 election
- 2002: Abortive coup. Returns to power after two days
- 2011: Reveals he is being treated for cancer
- 2012 (October): Re-elected for another six-year term
- 2012 (December): Has fourth cancer operation in Cuba
- 2013 (February): Returns to Venezuela to continue treatment
- Obituary: Hugo Chavez
- Praise for ‘tough’ BBC interviewer
“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.
UK Foreign Minister William Hague said he was “saddened” to learn of the death, saying Mr Chavez had left a “lasting impression” on Venezuela.
The UK Foreign Office issued a travel advisory warning visitors to Venezuela: “This is a sensitive moment for the country. You are strongly advised to avoid any public gatherings.”
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.