The image of Colombian businessman Alexander Saab is projected on a screen at the National Assembly, in Caracas on October 16, 2021. AFP
The Justice Department said in a statement that Alex Saab was due to appear in court in Florida on Monday and expressed "admiration" to authorities in Cape Verde for their help in the case.
Venezuela reacted furiously, suspending talks with the US-backed opposition on ending the country's political and economic crisis.
Saab, a Colombian national, and his business partner Alvaro Pulido are charged in the United States with running a network that exploited food aid destined for Venezuela, an oil-rich nation mired in an acute economic crisis.
They are alleged to have moved $350 million out of Venezuela into accounts they controlled in the United States and other countries. They risk up to 20 years in prison.
Saab, who also has Venezuelan nationality and a Venezuelan diplomatic passport, was indicted in July 2019 in Miami for money laundering, and was arrested during a plane stopover in Cape Verde off the coast of West Africa in June 2020.
Venezuela's opposition has described Saab as a frontman doing shady dealings for the populist socialist regime of Maduro.
Colombian President Ivan Duque praised Saab's extradition.
"The extradition of Alex Saab is a triumph in the fight against the drug trafficking, asset laundering and corruption that the dictatorship of Nicolas Maduro has fostered," Duque tweeted.
Venezuelan opposition leader Juan Guaido, who is recognized as the country's acting president by the United States and more than 50 other countries, also welcomed the move.
"We Venezuelans, who have seen justice kidnapped for years, respect and celebrate the system of justice in democratic countries like Cape Verde," he tweeted.
In a development not officially linked to the Saab extradition, shortly after news broke of the extradition six former oil executives under house arrest for corruption in Venezuela were taken to an undisclosed prison.
They had worked for Citgo, a US-based subsidiary of the state oil company PDVSA. Five of the six hold US nationality and the other is a permanent resident of the United States.
"American detainees in Venezuela are now being used as political pawns," said US Democratic Party heavyweight Bill Richardson, who led an unsuccessful mission to Venezuela to seek the executives' release last year.
Richardson has managed international negotiations for a number of high-profile American detainees.
"We will continue to press for their release," he said.
Cape Verde agreed last month to extradite Saab to the United States, despite protests from Venezuela.
Venezuela said Saab had been abducted by Washington.
"Venezuela denounces the kidnapping of the Venezuelan diplomat Alex Saab by the government of the United States in complicity with the authorities in Cape Verde," the Caracas government said in a statement.
The speaker of Congress, Jorge Rodriguez, said the government would not attend the fourth round of talks with the opposition due to start Sunday in Mexico City "as a deep expression of our protest against the brutal aggression" against Saab.
Rodriguez leads the government delegation for the negotiations and had hoped to make Saab one of its members until his arrest.
Venezuela had called Saab's arrest in Cape Verde "arbitrary" and claimed he was suffering "mistreatment and torture" at the hands of the Cape Verde authorities.
Roberto Deniz, a journalist who has covered Saab's story for the Venezuelan investigative news site Armando.info, said last month that the regime in Caracas was desperate to get him released.
"It is clear that there is a lot of fear, not only because he may reveal information about bribes, about the places where money was moved and the inflated pricing," Deniz said, but also because Saab "was the bridge for many of these deals that the Maduro regime is beginning to carry out with other allied countries."
Venezuela's former attorney general Luisa Ortega, who broke with the regime and fled the country, said Saab was "the main figurehead of the regime," adding that she herself had passed on evidence in the case to "some authorities."