Bears general manager Phil Emery told reporters last week that the club expected to sign Palmer to serve as the backup to Josh McCown after starter Jay Cutler tore a groin muscle against the Washington Redskins on Oct. 20.
Cutler will be out a minimum of four weeks.
Originally selected by the Redskins in the sixth round of the 2007 draft, Palmer completed 12 of 18 attempts for 116 yards and a touchdown for the Bears in the preseason but failed to earn a spot on the final roster.
Grant has appeared in 66 games with 11 starts over five seasons with the St. Louis Rams and San Francisco 49ers. The 6-foot-1, 251-pound linebacker has 64 career tackles and 29 career stops on special teams. Grant has also registered five sacks, four forced fumbles, two fumble recoveries and five pass break-ups.
Both Palmer and Grant practiced with the Bears on Monday following the team's bye weekend.
The Bears also signed wide receiver Terrence Toliver to the practice squad and terminated the practice squad contract of wideout Ricardo Lockette.