The deal is for the slotted amount of $18 million guaranteed over four years. A source told Schefter that the contract should include about $11 million in bonuses.
Selected with the eighth overall pick in the draft, Smith was the last unsigned rookie in the NFL. Part of the reason for his holdout was language in his contract that would allow the team to reclaim guaranteed money if the linebacker is suspended under the NFL's new helmet-contact rules, a source previously confirmed to ESPN.
Smith is expected to report as early as Monday night and could play in the Bears' next preseason game Saturday at the Denver Broncos, a source told Schefter.
The Bears said in a statement Monday that Smith will be available to the media on Tuesday, but they did not announce his signing.
Asked Sunday whether missing all of camp would limit Smith's ability to be a defensive field general on opening day, Bears coach Matt Nagy did not mince words.
"I think it does," Nagy said. "You're playing at that position, and there are a lot of calls that go on -- very similar to a quarterback, there's a lot going on. But I have full confidence in [defensive coordinator] Vic [Fangio] and his staff that when he does get here, they'll get him up to speed, and whenever that is, we'll see.
"But again, that's why we all get paid as coaches is to try to help our players out as much as possible, and that's kind of where we're at."
Smith, a University of Georgia product, was named SEC Defensive Player of the Year and a consensus All-American last season, and he was expected to start immediately at one of the Bears' linebacker spots.
Smith's speed (4.51-second 40-yard dash at the NFL combine) also lends itself to the rookie's staying on the field on passing downs. One of Smith's strengths at Georgia was his ability to run with tight ends in coverage.
ESPN's Jeff Dickerson, Nick Friedell and The Associated Press contributed to this report.