The move Wednesday came five days after the Broncos signed Anderson to an offer sheet. Terms of the deal weren't released.
"I think the most important thing for me was that I got the sense that I was wanted by the Texans organization," Anderson told the Texans' Web site. "I always knew they liked me, but I never knew what type of commitment they had for me as a player. I think that's the ultimate comfort level to know that your coaches like you and they are committed to you. I am looking forward to getting to play my best and continue to help this offense flourish. We have so many weapons on this offense; that's what's so exciting about being on this team."
A seventh-round draft pick in 2006, Anderson has 399 yards and three touchdowns in his three-year career.
The Associated Press contributed to this report.