Smith, who was selected eighth overall in April, was the only remaining unsigned pick of the 2018 NFL Draft.
The four-year contract was worth $18.4 million, with multiple media outlets reporting that it included $11.5 million guaranteed. Like all rookie deals, it included a team option for a fifth season.
"We're looking forward to Roquan joining our team and getting him prepared for the 2018 season," Bears general manager Ryan Pace said.
Smith, a linebacker, missed the Bears' entire training camp and the team's first two preseason contests.
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, ESPN reported.
Per the Chicago Tribune, Smith is expected to join the Bears for their joint practices against the Denver Broncos beginning Wednesday in Englewood, Colo.
Smith helped lead Georgia to the national championship game last season, winning the Butkus Award as the top linebacker in college football as well as SEC Defensive Player of the Year honors.
The 6-foot-1, 225-pound Smith also was a finalist for the Bronko Nagurski Trophy and Chuck Bednarik Award, both of which are presented to the country's top overall defensive player.
Smith amassed 137 tackles, including 14 for loss, 6.5 sacks and two fumble recoveries during his stellar junior season. He also was named Defensive MVP of the Rose Bowl in the College Football Playoff semifinal with 11 tackles as the Bulldogs defeated Oklahoma to advance to the national championship game.
Smith was projected to step in immediately for the Bears and play alongside fellow linebacker Danny Trevathan.