Gunter decided to return to Arizona after making a free-agent visit with the Green Bay Packers last week.
The Cardinals also signed offensive linemen Andrew Lauderdale (Arizona Hotshots) and Jeremiah Poutasi (Salt Lake City Stallions), who had both played in the Alliance of American Football.
Gunter, 27, is coming off his best season as a pro with the Cardinals, finishing with career highs in sacks (4.5), tackles (44) and forced fumbles (two). While he played in all 16 games for the fourth straight season, he started 10, the second most of his career.
A fourth-round draft pick (116th overall) of the Cardinals in 2015, Gunter was used primarily in sub packages. Of his 614 defensive snaps, 522 (85 percent) were in nickel.
Gunter went to Delaware State, a FCS school. For his NFL career, he has eight sacks and 95 tackles.
ESPN's Josh Weinfuss contributed to this report.