The leaders of neighbouring Latin America states were the first to hail Mr Chavez, who died aged 58 following a two-year battle with cancer.
His passing, which brought to an end his controversial 14-year rule, was confirmed by a visibly choked Vice-President Nicolas Maduro, who described it as a "moment of deep pain".
Mr Maduro added: "We were accompanying his daughters, his brother, his family members at the hospital, and we received the hardest and the most tragic of news that we will ever transmit to our people.
"At 4.25 in the afternoon of March 5, Comandante President Hugo Chavez Frias died."
The flamboyant Mr Chavez had undergone four operations in Cuba, as well as gruelling chemotherapy and radiation treatment, for the disease that was first detected in his pelvis in mid-2011.
His latest surgery was carried out before Christmas and he had not been seen in public since.
Mr Chavez flew back to Venezuela from Cuba last month and was taken straight to a military hospital in Caracas where he has been receiving treatment.
He is understood to have been suffering badly from a respiratory infection in recent days.
The leader will be given a state funeral in Caracas, with the service likely to be attended by millions of supporters and left-wing leaders from across the globe.
US President Barack Obama called for a new relationship with Venezuela.
He said: "The United States reaffirms its support for the Venezuelan people and its interest in developing a constructive relationship with the Venezuelan government.
"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."
Peru's President Ollanta Humala said: "Adios commander and friend Hugo Chavez. My condolences to his family and to the entire Venezuelan people."
Haiti's leader Michel J Martelly said: "I extend, on behalf of the people of Haiti, my sincere condolences to the people after the death of Venezuelan President Hugo Chavez."
Chile and Ecuador also released official notes of condolences to Venezuela. Ecuador said it felt the loss as their own, and hoped that its neighbours could carry on Mr Chavez's revolution. Brazil's President, Dilma Rousseff, added that she was mourning the loss of a great "friend" of her country.
Mr Chavez was re-elected in October with 55% of the vote, but was too ill to be sworn in for his six-year term beginning on January 10. Venezuela's Supreme Court ruled he remained president, even in the hospital.
His style of leadership has proved controversial, with supporters backing his charismatic style, anti-US rhetoric and oil-financed policies that brought subsidised food and free health clinics to long-neglected slums, while opponents branded him an egotistical dictator.
His government provided substantial funding for the el Sistema musical foundation of 125 youth orchestras.
It has links to Scotland, through the Big Noise musical programme in the Raploch area of Stirling, which is a partner.
Despite sadness at his death, in some quarters of Venezuela, citizens set off fireworks in celebration.
An election for the new president will be held within the next month.
Mr Maduro has been named by Mr Chavez as his successor but he is likely to face fierce competition from the centre ground's Henrique Capriles.