Brandstater, cut by Miami, and Edison, who was with Seattle, were added to the roster in time for Sunday's practice.
Dallas had open roster spots after quarterback Zack Eskridge and nose tackle Billy Blackard were released Saturday.
Brandstater was drafted out of Fresno State by Denver in the sixth round in the 2009 draft. He was released last year after the Broncos drafted Tim Tebow and acquired Brady Quinn. Brandstater had since had time on practice squads in Indianapolis and Miami.
Edison, a Texas native who played at Stephen F. Austin, was drafted by Tennessee in 2009. He went to Seattle after being released by the Titans this year.