Williams has been on the recovery from a torn patella tendon in his rookie season in 2011, but said that his move to the Cowboys will give him the chance to prove himself.
"Right now, it's kind of like the baby step phase," he told the club's official website. "I've got to learn a whole new system, and I've got to get comfortable in the system - I've got to learn pass protections, I've got to be a great student of this offense before I can go out there and show what I'm capable of doing.
"It's just one of those things where sometimes you've got to dig down, get healthy, come back out and shut everybody up - prove everybody wrong."
Williams has spent his career so far with the Arizona Cardinals.