The move that creates competition for Kellen Moore was announced Thursday.
Archer was cut as a rookie free agent by the Minnesota Vikings two years ago. He plays for the Georgia Force in the Arena Football League.
The former William and Mary standout will likely get a chance to compete with Moore - an undrafted rookie from Boise State - to be the team's third-string quarterback behind Matthew Stafford and Shaun Hill when training camp begins next month.
Burrell is an undrafted rookie from Wayne State. He is a native of Port Huron.