An American working for a covert U.S. program in Cuba was sentenced Saturday to 15 years in prison in the island, the Cuban government said, a verdict that promises to further disrupt relations between the two countries.

Alan Gross, 61, worked as a contractor for a USAID program that secretly provided technology like computers and communications equipment to encourage democratic reforms. He was arrested in late 2009 and accused of aiding Cuban "subversives" and working to overthrow the government. Prosecutors had originally...