Lewis played in every game last season for the Kansas City Chiefs with 15 starts. He had 56 tackles, including three for losses, and an interception.
Lewis, 25, had spent his entire four-year NFL career with the Chiefs after being drafted in the fifth round in 2010.
Lewis has started 50 games, including all 16 in 2011, when he tied a career high with three interceptions.
The move comes at the end of a busy 24 hours for the Texans, who signed quarterback Ryan Fitzpatrick on Thursday night before trading quarterback Matt Schaub to the Oakland Raiders on Friday for a sixth-round pick in this year's draft.