The person spoke on condition of anonymity because the trade had not been announced.
Smith, the NFL leader in tackles so far this season, joins a Baltimore team that has won two in a row and sits atop the AFC North.
The Ravens have had their issues defensively this season, but they've improved in that area and now add a second-team All-Pro to their linebacking group.
It's the Bears' second major trade involving a defensive player in less than a week. They dealt three-time Pro Bowl defensive end Robert Quinn to Philadelphia for a 2023 fourth-round pick on Wednesday.
Smith was at the dais addressing reporters when reports of the Quinn trade surfaced. He became emotional and cut the session short.
On Monday, Ravens coach John Harbaugh held his usual weekly news conference - shortly before the news of the Smith trade broke. He was asked is he anticipated a move before Tuesday's trade deadline.
''If I did, then the cat would be out of the bag,'' he said.
The 25-year-old Smith has 83 tackles and 2 1/2 sacks this season. A first-round pick by Chicago in 2018, he has 16 1/2 sacks in his career.
With his rookie contract set to expire, Smith was hoping to strike a new deal. He participated in voluntary and mandatory offseason workouts, but with negotiations at a standstill with the Bears, things took a heated turn once training camp started.
Smith, who does not have an agent, opted to ''hold in'' - attending meetings and practices without participating in drills. Tensions boiled over when he went public with a trade request.
He accused general manager Ryan Poles of negotiating in bad faith.
Smith eventually ended his hold-in and practiced for the first time on Aug. 20.
Now he joins the Ravens, who have led by double digits in every game this season and would have an even better record if not for some pretty bad fourth-quarter collapses.
Ravens linebacker Justin Houston already has six sacks on the season. Linebacker Odafe Oweh and defensive lineman Calais Campbell are also pass-rushing threats - and the Ravens added linebacker Jason Pierre-Paul in late September.
Baltimore won at Tampa Bay last Thursday, so the Ravens have extra time to prepare for next Monday night's game at New Orleans.
Harbaugh did have some bad news Monday, saying receiver Rashod Bateman could be out for a few weeks because of his foot injury. Also, running back Gus Edwards (hamstring) is day to day but could play against New Orleans.
The linebacking group could also receive a boost. Harbaugh said Tyus Bowser and rookie David Ojabo are set to be activated, and he thinks there's a good chance Bowser will be ready to play. Both Bowser and Ojabo have been out because of Achilles tendon injuries.
AP Sports Writer Andrew Seligman contributed to this report.
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