Premier Andrew Fahie was detained in Miami by US agents posing as cocaine traffickers from a Mexican drug cartel.
He agreed a $700,000 (£560,000) payment to allow traffickers to use BVI ports with an undercover informant, charges filed in the US said.
Foreign Secretary Liz Truss has said she was “appalled” by the allegations.
Mr Fahie, the elected head of government of the British overseas territory, was arrested by US Drug Enforcement Agency (DEA) officials in Florida, alongside senior BVI port official Oleanvine Maynard.
A third person, Kadeem Maynard – Ms Maynard’s son – was also arrested on Thursday in connection with the undercover DEA case.
The arrests were made after DEA agents pretended to be cocaine traffickers from Mexico’s Sinaloa Cartel – said to be the largest supplier of illegal drugs to the US market and formerly run by now-imprisoned drug lord Joaquín ‘El Chapo’ Guzmán.
The trio have been charged with conspiracy to import more than 5kg (11lb) of cocaine into the US and conspiring to commit money laundering, authorities said.
In a criminal complaint filed in a US federal court, reviewed by the BBC, the DEA said the investigation was launched in October based on work carried out by a confidential informant.
The informant is said to have claimed in meetings with Mr Fahie to be a cartel member aiming to smuggle thousands of kilograms of Colombian cocaine worth tens of millions of dollars through the BVI, with the drugs to be shipped to US Caribbean territory Puerto Rico and then on to Miami and New York.
Mr Fahie and the DEA informant also discussed setting up pre-arranged drug busts of money and low-quality drugs to make it look like the BVI leader was fighting crime in the islands, the charges said.
He told the informant during one meeting that the UK government had been trying for years to remove him from office, the documents claimed.
Mr Fahie is quoted as saying: “I have plenty of people, and I don’t sell them out to the British with their plans… they always want to capture people, but me I see what they are doing and I protect the people.”
He and Ms Maynard were later arrested on a visit to Miami, after being separately shown a private plane and designer shopping bags, which authorities said contained $700,000, according to the charges.
There have long been questions about the way the British Virgin Islands have been run.
Since January last year, Andrew Fahie has been the subject of an inquiry into allegations of misgovernment and corruption.
But now the premier of the British Overseas Territory is in custody, facing charges of drug trafficking and money laundering.
Foreign Secretary Liz Truss said the arrest demonstrated the importance of the commission leading the inquiry, whose report she expected to be published soon
The commission hit the headlines last year when it emerged Mr Fahie was being defended by a Conservative MP, the former Attorney General, Sir Geoffrey Cox.
The BVI is a British overseas territory made up of more than 40 islands, located in the Caribbean to the east of Puerto Rico.
It operates as a parliamentary democracy, with the premier acting as the head of the elected government alongside the governor, John Rankin, who is appointed by the UK government.
Leaks of documents known as the “Panama Papers” and “Paradise Papers” revealed the islands to be a popular tax haven.
‘Governance and corruption’
After being informed by the US government of the arrests, Ms Truss held talks with Mr Rankin – who is set to hold an emergency meeting of the territory’s cabinet later on Thursday.
She said: “This afternoon, the Premier of the British Virgin Islands, Andrew Fahie, was arrested in the United States on charges related to drugs trafficking and money laundering. I am appalled by these serious allegations.”
In January 2021 an independent inquiry into corruption in the islands was launched, amid long-standing allegations of state corruption.
In a statement, Mr Rankin confirmed the arrest was not related to the ongoing inquiry.
He declined to comment further, but added: “To avoid unnecessary speculation, I intend to move ahead urgently on publication of the inquiry report so the people of the BVI can see its contents and its recommendations in the areas it addresses.”
The BVI’s Deputy Premier Natalio Wheatly “will remain acting premier” of the territory, Mr Rankin said.
Mr Fahie and officials from the British Virgin Islands Ports Authority could not be reached for comment when contacted by Reuters news agency, and the premier’s office did not immediately respond to requests for more information.