Johnson, 31, was a first-round pick by the Kansas City Chiefs in 2003 and has rushed for 6,221 yards with 55 touchdowns over an eight-season career.
He played for the Chiefs for 6 1/2 seasons but was released midway through the 2009 season after making demeaning comments about Kansas City Coach Todd Haley. He appeared in seven games for Cincinnati in 2009 and two for Washington last year.
Johnson was twice selected for the Pro Bowl. He was second in the NFL with 1,789 rushing yards in 2006 after running for 1,750 yards in 2005.