In cutting Bailey, who two years ago led the team in tackles, the Giants save $857,000 in salary, putting them about $2 million below the NFL's $37.1 million cap.
Associated Press sources said that Croel signed a one-year, $850,000 deal.
Bailey's demise was the result of the Giants' switch from a 3-4 defensive front to a 4-3 alignment.
Bailey split time at middle linebacker in 1994 with Corey Widmer. He was third on the team with 70 total tackles, but the Giants wanted a more physical presence in the middle.
Michael Brooks will play the middle, with Croel, the 1991 NFL Rookie of the Year, on the outside.
* BALTIMORE FOOTBALL CLUB: The CFL team announced the signing of three linebackers, including Marlon Williams, a four-year starter at Georgia Tech.
Williams, 6 feet 2, 225 pounds, had 231 tackles, 17 sacks and five interceptions in 42 career games for Tech. Also signed were Maurice Gravely (6-4, 210) of Wake Forest and Les Barley (6-2, 225) of Winston-Salem State.
Gravely is a cousin of Baltimore linebacker Tracey Gravely. Barley, 27, split the last three seasons with Tampa Bay and Charlotte in the Arena Football League.