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 likely will get a chance to compete with Moore, an undrafted rookie from Boise State who set several college records, 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 out of Wayne State.