The younger Domenici announced Sunday in Albuquerque that he would join the Republican field for the statehouse race, the Albuquerque Journal reported.
The newspaper said it's the first try for elective office for Domenici, 50, an Albuquerque environmental lawyer.
"I am not a professional politician," he said. "I am an ordinary citizen who, like most New Mexicans, is frustrated and fed up with the unprecedented budgetary and corruption crises our state now faces."
With the announcement, Domenici joins a GOP field that already contains former state Republican Party Chairman Allen Weh, state House Rep. Janice Arnold-Jones of Albuquerque, public relations firm owner Doug Turner and District Attorney Susana Martinez of Las Cruces.
The Journal said Lt. Gov. Diane Denish is currently the lone Democratic candidate for governor.
Family members, including his father, surrounded Domenici during the announcement. The elder Domenici, one of New Mexico's most popular politicians, served as the state's U.S. Senator for 36 years before his 2008 retirement, the newspaper said.