Terms were not disclosed.
Smith, 32, rushed for a career-high 1,139 yards and tied for second in the AFC with 16 touchdowns in 2000 for the Miami Dolphins. He rushed for 968 yards the following year, but became expendable when the Dolphins traded for Ricky Williams in 2002.
Last season, he rushed for 737 yards and seven touchdowns in 11 games for the Carolina Panthers, but had personal problems and was given a paid leave of absence on Nov. 29. He eventually was placed on injured reserve with a shoulder injury on Dec. 18.
Smith participated in minicamp Monday, and will compete for a backup job to Green, who ranked fourth in the NFC with 1,240 yards rushing and also caught 57 passes for the Packers last season.
Green Bay also has signed receiver-returner Antonio Chatman, who broke the Arena Football League record for all-purpose yards with 3,678 in 18 games with the Chicago Rush. He caught 123 passes for 1,608 yards and returned 84 kicks for 2,062 yards.