The team is expected to announce Wednesday that it has signed the former Green Bay Packers running back. Grant tweeted Tuesday night that he's looking forward to helping the Redskins win.
Grant spent five seasons with the Packers. His best season was 2009, when he ran for 1,253 yards.
Grant worked out Tuesday for the Chicago Bears, according to a league source.
Grant, who will turn 30 in December, visited the Detroit Lions last week and put forth an impressive workout, according to the source.
Butler injured a hamstring in Sunday's 38-31 loss to the Bengals.
Defensive lineman Chigbo Anunoby was signed to the practice squad. Defensive lineman Delvin Johnson was released from the practice squad.
Information from The Associated Press and ESPNChicago.com's Michael C. Wright was used in this report.