The Nationals announced the move Friday.
Jennings will work on Washington's scouting operations.
He was fired in October by the Marlins, a team he had worked for since 2002.
Jennings had been Miami's general manager, then took over as manager in May, becoming the first big league manager with no experience in that job or as a player in the majors since Atlanta Braves owner Ted Turner managed his team for one game in 1977. Jennings was 55-69 as manager.
Before working for the Marlins, Jennings was Tampa Bay's director of scouting.