The 29-year-old Williams, who helps the Lions replace Haloti Ngata, likely would slide into a starting role and be in an interior line rotation with A'Shawn Robinson and Akeem Spence, who both started at defensive tackle after Ngata was lost for the season. With Ngata out of the lineup, Detroit's run defense suffered.
Ngata signed with the Philadelphia Eagles last week.
On a conference call Wednesday, Williams said he was not told what his role would be in Detroit and that they haven't talked about scheme. He said he signed with the Lions after meeting with some coaches and being "excited about the direction they were headed," as well as the opportunity he could have in the defense.
Williams was released on Saturday. He played just one season with the Tennessee Titans after signing a three-year, $16.5 million deal last offseason. He wasn't able to make as many splash plays or command double teams as much as the Titans expected him to, finishing the season with 20 tackles in 11 starts.
Williams, however, told ESPN that "my best football is ahead of me."
At 6-foot-2 and 313 pounds, Williams is a bit undersized for the nose tackle position, which may have hurt his ability to get off blocks for the Titans. He was a 2013 first-round pick by the Denver Broncos, with whom he spent four seasons.
In 75 career games (59 starts), Williams has six sacks and 114 tackles.
ESPN's Cameron Wolfe contributed to this report.