Richardson served as secretary of energy and ambassador to the United Nations under former President Bill Clinton, The Hill reported.
The Washington Post reported Obama will make the announcement at a Chicago news conference.
Richardson was one of three candidates for secretary of state. Obama picked his former rival, New York Sen. Hillary Clinton, over Richardson and Sen. John Kerry, D-Mass.
The newspaper said New Mexico Lt. Gov. Diane Denish, who already planned to run for the open governor's seat in 2010, will take over as the state's chief executive for the next two years.