Centers, who turns 35 in June, had 43 catches for 388 yards for the Bills last season, but with Travis Henry and Sammy Morris showing pass-catching ability in the backfield, Centers became expendable.
Robinson, who turns 33 in April, was third on the team last season with 102 tackles, but the offseason additions of outside linebackers Takeo Spikes and Jeff Posey squeezed him out.
Centers ranks ninth all-time in catches with 808 for 6,691 yards. No other running back in NFL history has more than 700 receptions.
The 13-year veteran signed as a free agent with the Bills in 2001, and caught 80 passes for 620 yards in his first season with the team. However, he caught barely more than half that total last season.
The three-time Pro Bowler set a single-season record with 101 receptions for 962 yards in 1995 for the Arizona Cardinals. He played nine years with Arizona and two seasons with the Washington Redskins before joining the Bills.
His departure means the Bills have lost 169 catches from last year's offense. Wide receiver Peerless Price had 94, and tight end Jay Riemersma had 32.
Buffalo signed Robinson as a free agent last April. He spent eight years with the Houston Oilers-Tennessee Titans franchise, and two seasons with the Jacksonville Jaguars, starting 148 games.
Often assigned to cover opposing running backs and tight ends, Robinson has recorded more than 100 tackles in a season six times. He had a career-high 165 for Jacksonville in 1996
Beautician charged with giving client fatal silicone butt injection
Duggar sisters unveil Christian dating rules in new book