Hayes was one of several veteran linebackers the Bears brought to Halas Hall for an official visit earlier in the week.
Hayes spent the past four seasons as a member of the Tampa Bay Buccaneers, with whom he started a total of 42 games. Originally a sixth-round draft choice by the Bucs out of Florida State, Hayes recorded a career-high 98 tackles in 2009.
The Bears were in the market for experienced depth at linebacker behind veteran starters Brian Urlacher, Lance Briggs and Nick Roach. Rounding out the depth chart at the position are two former undrafted rookie free agents, Dom DeCicco and Patrick Trahan; former St. Louis seventh-round selection Jabara Williams; the Bears' 2011 sixth-round pick, J.T. Thomas; and newly signed special teams ace Blake Costanzo.
Thomas spent his entire rookie season on injured reserve and was arrested in the offseason on a misdemeanor drug possession charge.
Urlacher and Roach both have one year remaining on their current contracts. Briggs recently was rewarded with an extension and is under contract through 2014.
The club may still opt to select a linebacker at some point in the upcoming NFL draft.
The Bears released receiver Max Komar, who appeared in two games and did not make a catch.