Galvez, also known as Caracol (Snail), was arrested in a restaurant in the western city of Medellin, Colombia's defence ministry said late Saturday.
He was then handed over to Peruvian authorities yesterday because of his "dangerousness" and flown back to his home country, Colombian national police chief Jorge Nieto told a press conference.
As he was escorted toward an awaiting Peruvian air force plane, Galvez repeatedly told journalists he had "the right to be presumed innocent."
Galvez "is described by Peruvian police and the United Nations Office on Drugs and Crime as Latin America's new 'Chapo' Guzman," the Colombian defence ministry said.
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The jailed Mexican drug lord, who formerly headed the powerful Sinaloa cartel, was captured in January after months on the run.
According to a wanted notice from Peruvian police, Galvez is "violent and aggressive" and headed a network "dedicated to extortion, aggravated robbery, illegal drug trafficking" and other assorted crimes.