Tren de Aragua has been labelled by the United States as a terrorist organisation.
Guerrero Flores was charged in a New York federal court with racketeering conspiracy and other crimes, including lending support to terrorists in crimes that stretched more than a decade, authorities announced in December.
US Attorney Jay Clayton said at the time the gang was responsible for countless acts of violence, extortion and drug trafficking in North America, South America and Europe. Trump on Thursday nominated Clayton to be director of national intelligence.
The US State Department had offered rewards of up to $US5 million ($A7.1 million) for information leading to Guerrero Flores' arrest
In a post on his social media site on Friday, Trump wrote, "Tren de Aragua terrorists no longer have safe haven in Venezuela or anywhere else and, under my leadership, we will find these vicious murderers and drug lords anytime, anyplace, and send them to the depths of hell where they belong."
Trump has taken a series of extraordinary actions against the gang, including a series of strikes on small boats his administration has accused of smuggling drugs to America.
Trump and administration officials have consistently blamed Tren de Aragua for being at the root of the violence and illicit drug dealing that plague some US cities.
The president spent months repeating the claim — contradicted by a declassified US intelligence assessment — that Tren de Aragua had operated under Venezuelan President Nicolás Maduro's control.
The US whisked Maduro out of Venezuela to face US drug charges in January.
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