ESPN reported Friday that Johnson would receive a five-year contract worth $750,000 per year.
Johnson has an 8-year record at Furman of 60-36, including 30-9 in the last three years. His 2001 Furman Paladins team finished as national runners-up in Division I-AA, losing Friday night's national championship game to Montana 13-6.
Johnson, 51, a native of Columbia, S.C., played college football at Furman and has been in coaching for 24 years. Before accepting the head coaching job at Furman in 1994, he served as defensive coordinator at Clemson for one year, and at Furman as defensive coordinator. Johnson was defensive coordinator for Furman's Division I-AA national championship team in 1988.
Woody Widenhofer resigned as Vanderbilt coach on Nov. 8 after five years at the school. He was 15-40 in five seasons and 4-36 in Southeastern Conference games, with just one league victory in the past two seasons.