The third-year offensive lineman has started 24 of 32 games played for the Bears since being claimed off the Philadelphia Eagles practice squad as a rookie in 2002.
Edwards played in 15 games for Chicago in 2004, totaling eight starts between both guard positions.
An undrafted free agent out of Central Florida, Edwards started all 16 games for the Bears at left guard in 2003 despite switching to guard from tackle the week before the start of the regular season.
He split his rookie season of 2002 between Philadelphia and Chicago, but made his NFL debut against Tampa Bay on December 29, 2002.
Along with Edwards and Bobby Gray the Bears still have three restricted free agents to sign their one-year tender offers. Guard Terrence Metcalf, tight ends John Gilmore and John Owens have yet to do so, but are expected back with the team.