The 26-year-old Herron was drafted by Pittsburgh in the seventh round in 2005. He has rushed for 273 yards, caught 29 passes for 211 yards and scored five touchdowns in 23 career games with Green Bay and Tampa Bay.
The 5-foot-11, 225-pounder could fill Wright's role as a part-time back behind Jamal Lewis. Wright signed a two-year contract with Arizona on Tuesday.
Coincidentally, Wright and Herron were teammates at Northwestern.
Herron played 16 games for the Packers in 2006. He spent all of 2007 on Green Bay's injured reserve list with a knee injury and was inactive for all four games he was on Tampa Bay's roster last year.