Chicago also signed wide receiver Demarcus Ayers to the practice squad and placed Floyd on injured reserve. The moves were announced on Thursday.
Floyd, the Bears' first round pick in the 2016 NFL Draft, suffered a season-ending right knee injury in the Bears' Week 11 loss to the Detroit Lions. He had 34 tackles, 5.5 sacks, two passes defensed and a fumble recovery in 10 starts this season.
Jones, 27, spent his first two NFL seasons with the Tampa Bay Buccaneers. The 6 foot 4, 238 pound defender had one tackle and a fumble recovery in eight games last season for the Buccaneers. Jones had 14 tackles, five sacks, a forced fumble and a fumble recovery in 2015 with Tampa Bay.
On Monday, Bears coach John Fox hinted that Floyd's move to injured reserve could be coming.
"I think he's going to miss some time," Fox told reporters. "The exact extent of all the medical terms, I think it's just fair to say he's going to miss some time. They're still evaluating it."
"He's one of our top players," Fox said. "Obviously it's disappointing. He was having a heck of a game. He was playing extremely well. It's unfortunate, but it's reality."
The Bears face the 9-1 Philadelphia Eagles at 1 p.m. Sunday at Lincoln Financial Field.