To make room for Johnson on the roster, the team waived 25-year-old cornerback Shaun Prater, who signed as a free agent on Tuesday.
Johnson was cut from both Cincinnati's and New York's roster this preseason.
A fifth-round selection by the Buccaneers in the 2008 draft out of San Diego, Johnson last appeared in a regular-season contest in 2013 with the Bengals.
Over 29 career NFL games, Johnson has completed 96 of 177 passes for 1,042 yards, five touchdowns and 10 interceptions.
The Colts (1–2) will host the Jaguars (1–2) at 1 p.m. ET on Sunday.
- Kayla Lombardo