Forte will replace Chris Ivory, who has agreed to sign with theJacksonville Jaguars.
Forte will also be reunited with former Bears teammate Brandon Marshall.
Forte leads the NFL in all-purpose yards (12,718) since he entered the league in 2008, but the Bears informed the 30-year-old running back in February that they would not offer him a contract to return.
He played eight seasons in Chicago, where he ranks as the second-most-productive tailback in franchise history behind only Hall of Famer Walter Payton.
Despite missing three games in 2015 with an MCL sprain, Forte still rushed for a team-high 898 yards while catching 44 passes for 398 yards.
A two-time Pro Bowler, Forte caught 102 passes two years ago -- an NFL record for a running back.
The Bears selected Forte out of Tulane in the second round of the 2008 NFL draft.