Terms were not disclosed for Van Pelt, who was eligible to become an unrestricted free agent on March 1.
Van Pelt joined the Bills in 1994 and saw limited playing time before Johnson broke his collarbone against the New England Patriots on Nov. 11.
The Bills were 2-6 in their final eight games under Van Pelt, who completed 58 percent of his passes for 2,056 yards with 12 touchdowns and 11 interceptions.
The 31-year-old Van Pelt could emerge as the starter next season. Johnson has one year left on his contract worth $11.2 million against the salary cap and recently was left available for next month's expansion draft.