ESPN's Chris Mortensen reported that Anderson will be brought in as soon as Monday to back up Josh Allen, who was the seventh overall pick of the 2018 NFL Draft.
Nathan Peterman, who started the season opener against the Baltimore Ravens, has served as the backup to Allen for the Bills.
Anderson has spent the last seven seasons backing up Cam Newton with the Carolina Panthers. Bills general manager Brandon Beane and head coach Sean McDermott were both in the Panthers organization before being hired by Buffalo last year.
The 35-year-old Anderson had a Pro Bowl season with the Cleveland Browns in 2007, when he passed for 3,787 yards and 29 touchdowns.
Anderson has completed 867-of-1,604 pass attempts for 10,413 yards with 60 touchdowns and 60 interceptions in 76 career games with the Arizona Cardinals, Browns and Panthers.
Allen has thrown for 666 yards with two touchdowns and four interceptions in four games this season entering Sunday's home game against the Tennessee Titans.
The 6-foot-5, 237-pound Allen passed for 1,966 yards with 19 touchdowns last season at Wyoming. He ran the 40-yard dash at the NFL Scouting Combine in 4.75 seconds with a 33 1/2-inch vertical jump.