League sources told the Houston Chronicle that Williams would make the stop and that he is now healthy.
Williams, 27, was a second-round pick by the Buffalo Bills in the 2011 NFL Draft. He played six seasons in Buffalo, registering 256 tackles, 36 passes defended, seven interceptions, three forced fumbles, a fumble recovery and a touchdown in 59 games.
The former Texas standout visited the Jacksonville Jaguars in May. He left Jacksonville without a deal, despite his link to Jaguars coach Doug Marrone. Marrone coached Williams and the Bills in 2013 and 2014.
The Bills cut Williams in March.
Williams has found it tough to stay on the field in the last few seasons, dealing with numerous neck injuries. He has played in 10 of a possible 32 games since 2014.
"Is it always in the back of my mind? Of course. It's my neck," Williams told the Bills' website in July. "It's something that's life threatening, but at the same time if I wasn't 100 percent sure of being out there I wouldn't be out there. I'm out there and whatever happens, happens. I believe things happen for a reason. With that being said I just have to enjoy what I have in front of me right now."
Williams had surgery in 2015, but has since said he is not retiring.
"Once again I'm NOT retiring but I am going to return better than ever," Williams tweeted on March 10. "Now, it's the waiting game."
Once again I'm NOT retiring but I am going to return better than ever. Now, it's the waiting game ⏰ #TickTick— Aaron Williams (@ajwilliams23) March 10, 2017
Williams began his career as a cornerback, but switched to strong safety in 2013.
The Texans currently have Corey Moore, Eddie Pleasant and Kurtis Drummond at strong safety. Houston's free safety stock includes Andre Hal, K.J. Dillon, Lonnie Ballentine and fifth-round draft pick Treston Decoud. Pleasant signed with the team as a free agent in March.
The Texans had the second-best pass defense in football last season, behind the Denver Broncos. Houston allowed the lowest first down percentage in the NFL. The Bills allowed the second-fewest touchdown passes in the AFC in 2016, trailing the Broncos in that category.