HIALEAH, Fla.—Ferrying Cubans to the U.S. in the past year has become a billion-dollar business involving airlines, charter operators and travel agents working from strip malls in Florida to airports across Central America and the Caribbean.

Immigration figures show a quarter of a million Cubans have arrived in the U.S. in the past year. Many of them paid thousands of dollars each to get away from the communist island and its crumbling economy, flying to Nicaragua and then paying coyotes, or migrant smugglers, to guide them across Mexico to the U.S. border.