Hayden's contract is worth a veteran minimum $825,000, according to a source familiar with the situation.
Hayden, a seven-year NFL veteran out of the University of Illinois who visited the Bears at the onset of free agency, was a second-round draft choice of the Colts in 2005. Hayden has made 47 career starts in stops with Indianapolis (2005-10) and Atlanta (2011), recording 11 interceptions, 41 passes defended and four forced fumbles. His most memorable professional moment came in the Colts' Super Bowl XLI victory over the Bears when Hayden picked off a pass and returned it 56 yards for a touchdown.
Hayden started a career-high 16 games for Indianapolis in 2007, but has missed 26 regular-season games in the past four seasons because of hamstring, knee and neck injuries. He signed a five-year, $43 million contract with the Colts in 2009, but was released after two seasons and landed on injured reserve at the end of 2010 because of the neck problem.
A Chicago native and Hubbard High School product, Hayden visited numerous teams last summer, including the Bears, before eventually landing with the Falcons. Hayden played in just eight games for Atlanta in 2011, making one start and intercepting two passes.
Wilhite spent last season as a member of the Denver Broncos, where he appeared in 15 games and made a pair of starts. A 2008 fourth-round choice of the New England Patriots, Wilhite appeared in 54 games for New England with 15 starts and four interceptions. Wilhite also has experience playing special teams.
If Hayden stays healthy, he might be given an opportunity to compete with Tim Jennings, who the Bears re-signed to a two-year deal, for the starting cornerback job opposite Charles Tillman. Hayden and Jennings were teammates while both were in Indianapolis.
ESPNChicago.com's Michael Wright contributed to this report.