Terms of the contract were not disclosed.
A linebacker out of LSU, Minter earned All-SEC first-team honors after leading the Tigers with 130 tackles, which was the fourth-best single-season total in school history. He also tallied five passes defensed, one forced fumble and one interception.
Minter was a Butkus Award finalist as the nation's top linebacker following the 2012 season.
Minter is the fifth Cardinals draft pick to sign, leaving first-round pick Jonathan Cooper, third-round pick Tyrann Mathieu and fourth-round picks Alex Okafor and Earl Watford left.