Anderson was cut by Chicago on Tuesday. The 6-foot-4, 255-pound lineman had 12 sacks as a rookie in 2006, helping the Bears reach the Super Bowl. He had only nine sacks over the next three seasons and has none this year.
The Texans signed Denney as a free agent after backup defensive end Connor Barwin broke his ankle in the season opener. Denney was inactive for last week's game against Oakland.
Houston has been looking for a defensive end to complement All-Pro Mario Williams, who has five of the team's nine sacks this season.