BOGOTÁ, Colombia—Retired Venezuelan Gen. Cliver Alcalá turned himself in to the U.S. counternarcotics authorities Friday, a day after U.S. prosecutors indicted him and other Venezuelan officials, including President Nicolás Maduro, on drug-trafficking charges, according to four people familiar with the matter.

Mr. Alcalá, 58, waived extradition and surrendered to Colombian authorities. Agents of the U.S. Drug Enforcement Administration accompanied him on a flight from Colombia to New York, where he is expected to collaborate with U.S. prosecutors building cases against other Venezuelan regime figures accused of having links to narco-terrorist groups, the people said.

“I’m sure he’s had face-to-face discussions with Maduro,” one high-ranking U.S. official said, referring to Mr. Alcalá as the “best kind of witness.”

Once a confidant of the late socialist leader Hugo Chávez, Mr. Alcalá broke ranks with Mr. Maduro in 2016 and has lived for the past two years with his family in an apartment in an upscale district of the Colombian port city of Barranquilla. Swapping his military fatigues for flashy suits and watches, Mr. Alcalá had become a vocal critic of Venezuela’s slide into authoritarianism under Mr. Maduro and had publicly said he was actively working to flip military officials in his home country against the strongman.

But on Thursday, the U.S. government unveiled a $10 million reward for Mr. Alcalá’s capture for his alleged role in permitting Colombian cartels to move cocaine through Venezuela and converting the country into a major transit hub in the global narcotics trade.