Tennessee Gov. Bill Haslam has signed legislation prohibiting local governments from passing antidiscrimination policies that go beyond state law, a measure that overrides a new gay-rights ordinance in Nashville.

The law, signed Monday, is meant to cut down on paperwork for businesses by making antidiscrimination policies uniform across the state, Mr. Haslam, a Republican, said in Chattanooga Tuesday. "We just don't think local governments should set HR [human resources] policies...