Webb, who was already signed for next year, is now locked in for the next six seasons.
"It feels amazing," he said. "I feel blessed and proud. Now I can relax and play ball and not worry about anything. This settles my mind down."
Webb intercepted a career-high five passes in the regular season and broke a team record with three interceptions in the playoffs. He had a career-high 68 tackles and 20 pass deflections and emerged as one of the NFL's top young cornerbacks.
A former third-round draft pick from Nicholls State, Webb also forced a fumble and had 1 1/2 sacks last season. In three NFL seasons, Webb has 164 tackles, seven interceptions, two sacks and 37 pass deflections.