Williams, 32, visited the Steelers on Friday and became the first outside free agent the Steelers have added in what had been a quiet week before the team announced that it had signed quarterback Ben Roethlisberger to a new contract.
Bell led the AFC with 1,361 rushing yards last season and was a first-team All-Pro selection. But he is expected to miss the first two games of next season, stemming from his arrest last August for marijuana possession and driving under the influence.
The only other running backs on the Steelers' roster are Dri Archer and Josh Harris and each played sparingly as rookies last season.
Williams said he will accept whatever role the Steelers plan for him and that he is energized by the opportunity to playing for a team that is coming off an 11-5 season and AFC North title.
"I haven't played in any Super Bowls," Williams said, "and to know this is a Super Bowl-contending team and to help them make that offense even better, it excites me and I hope that it excites Steelers Nation. I know we're going to do great things here."
The Panthers saved $2 million in salary-cap space by designating Williams as a post-June 1 cut.
Williams told Charlotte's WBTV that as a result of the way the organization treated the death of his mother to breast cancer in May that he wasn't upset when told he would be released. He said Greg Hardy was the only member of the organization to attend his mother's funeral.
Williams had been with Carolina since it made him the 27th pick of the 2006 draft. He has 6,846 career rushing yards and 46 rushing touchdowns. Injuries limited him to six games in 2014.
ESPN.com Panthers reporter David Newton contributed to this report.