The Chicago Tribune reported Sunday the deal will pay the four-year veteran $36 million. The report added that he declined to discuss his likely signing bonus.
The signing was a surprise because it was thought Briggs had fallen out of favor with Chicago management when he badmouthed the Bears after he was given the franchise tag last offseason, saying he would never play for Chicago again.
Late in the 2007 season, he changed his mind.
"I can see myself (back with the Bears), yeah," he said last December. "If things work out that way, which I hope they will, then I'll be back."
The former third-round draft pick made 140 tackles (10 for a loss).
Various reports said that either Washington and San Francisco were his next employers.