A veteran Senate staffer has been indicted as part of a probe related to the unauthorized disclosure of classified information that has also obtained the records of a New York Times reporter.

James A. Wolfe, the longtime head of security for the Senate Intelligence Committee, was arrested late Thursday, federal prosecutors said. Mr. Wolfe was indicted on charges of “making false statements to special agents of the FBI during the course of an investigation into the unlawful disclosure of classified information,” prosecutors...