The Chicago Tribune's Dan Pompei first reported the news.
Williams, 30, spent the first nine years of his NFL career with the Broncos but was suspended multiple times last season and appeared in just seven games. He was set to make $6 million in 2013, which prompted Denver to release him the day before free agency began.
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“We appreciate the contributions made by D.J. Williams during his time with the Broncos,” Broncos executive John Elway said at the time. “He was a solid player with this team for a number of years, showing a lot of versatility at linebacker. Our organization wishes D.J. all the best going forward.”
And now Williams, a 2004 first-round pick, has signed a one-year deal, according to Pompei. It includes a base salary of $900,000, and he can earn a maximum of $1.75 million through incentives. None of the money is guaranteed.
While not a long-term solution, Williams' addition does allow the Bears some flexibility next month -- middle linebacker is no longer a draft-day must-have.
Urlacher, meanwhile, plans to continue his career after passing on the Bears' take-it-or-leave-it one-year, $2 million offer.
"I get a chance to look around and see what's out there, if there's anything out there at all," he said Friday on the Dan Patrick Show. "I don't know; maybe nobody wants me. Who knows? We're going to find out, I know that much. ...
"It was hard for anyone to believe I wouldn't be [in Chicago]," he told the Chicago Sun-Times. "But I'm going to play for sure."
As for Williams, here's a little advice: Study your playbook but try not to tweet out pictures of it.