Nichols, who turns 32 next month, is the youngest head coach in NCAA Division I.
Davidson fired Coach Tripp Merritt with two games left in the 2012 season, which ended with a 2-9 record for the Wildcats.
Merritt had a 31-51 record over eight seasons -- 2005-12-- at Davidson.
The Davidson position is the first head coaching job for Nichols, who has been an assistant at Ohio State, Marshall and Toledo. He most recently was director of player personnel at Illinois.
Nichols owns Davidson school records for career passing yards (5,822), completions (465) and touchdown passes (51). The Wildcats were 22-6, including 10-0 in 2000, with Nichols as a starter.