The 6-foot-3, 327-pound nose tackle from Tennessee is expected to join in team meetings and participate in the Cardinals' practice on Tuesday.
Williams, the 26th pick overall, will be groomed to play between Darnell Dockett and Calais Campbell on Arizona's defensive front. At first, though, he will be behind two-year starter Bryan Robinson on the depth chart
Coach Ken Whisenhunt likes to slowly work his first-round picks into the lineup, making them earn the spot. He did that with cornerback Dominique Rodgers-Cromartie two years ago and running back Beanie Wells last season.
Williams played in a 4-3 defense in college but will shift to a 3-4 alignment with Arizona.
He was an all-SEC first-team selection last season, when he had 70 tackles, including 2½ sacks with nine tackles for loss and nine quarterback pressures.
During the draft, Whisenhunt said one thing stood out when looking at Williams.
"This guy has 70 tackles," Whisenhunt said, "so for me that shows an ability to redirect, chase plays to make tackles, a very active guy. When you combine that with his size. ... That's really something that's intriguing to us. As I made the comparison to basketball the other day, to me he's like a 7-footer who can play."
Earlier Monday, Whisenhunt said he knew Arizona was close to an agreement with Williams on Sunday night. There were widespread reports of an agreement through the day on Monday, including a Twitter message from Dockett, but the team didn't make it official until late in the afternoon Arizona time, in the midst of the team's second practice of the day.
After practice, Whisenhunt was asked if Williams' participation in summer workouts would mitigate the time he has lost in missing three days of training camp.
"No," Whisenhunt said. "We got some good work in the last couple of days and I don't think you can make that up but he's sure going to try."
He said Williams' earlier workouts gave him a lesson in what is expected of an NFL player.
"I think he got it," Whisenhunt said. "I think he more and more understood what he has to do. The big test now will be to see where he is with his weight and where he is with his conditioning because he's had a period since July, about the 12th, off. The real challenge is to see what you have to do to get him ready to go."