Taylor is now on track to start Sunday's season opener against the New York Jets. He returned to practice Monday after suffering a concussion in an Aug. 26 preseason game in Baltimore.
The Bills placed quarterback T.J. Yates on injured reserve Tuesday. Yates also suffered a concussion in the preseason loss to the Ravens and returned to practice Monday. He is eligible to return from injured reserve in eight weeks.
Webb is expected to take over Yates' role as the No. 3 quarterback.
In three preseason games, Taylor completed 48 percent of his passes for 100 yards, two interceptions and a 27.9 quarterback rating.