Morris went to college at Texas State, and played in 13 games with the San Francisco 49ers in 2013 as he was undrafted.
In his 13 games with the 49ers, who reached the NFC Championship game last season, Morris had one fumble recovery, along with five tackles.
Morris, 23, is 5-10 and weighs 188 pounds.
He also played in three games in the preseason, having one tackle.
While at Texas State, his best season was his final year in 2012 where he totaled 61 tackles (46 solo) with four interceptions.
Houston has made over 25 transactions in the past 24 hours, including he release of backup quarterback Case Keenum, along with trading what is now being said a 7th sound draft pick for New England Patriots backup QB Ryan Mallett.
The Texans are also to be said bringing back former safety Danieal Manning, who was released by the Cincinnati Bengals on Saturday.
Houston opens the season a week from today (Sunday) when the host the Washington Redskins in Week 1. This will be an NFC East vs. AFC South matchup.