The deal -- which includes $25 million guaranteed, per ESPN's Adam Schefter -- cannot become official until the new league year begins on Wednesday.
Robinson is coming off tearing an ACL in his left knee on the third play from scrimmage in the Jacksonville Jaguars' season-opening 29-7 win over the Houston Texans.
The 24-year-old cited new Bears coach Matt Nagy as one of the reasons he selected the Windy City as a landing spot, per ESPN's Josina Anderson.
"I like what coach Nagy did from an offensive standpoint in Kansas City," Robinson said, per Anderson on Twitter. "Me being able to see what he did in KC, being able to know that he is an offensive-minded coach seeing what he's done before (helped me)."
The Bears ranked third-worst in average yards per game (287.4) and dead last with 175.7 passing yards per contest. By comparison, the Chiefs -- under Nagy -- finished sixth in points (25.9) and fifth in total offense (375.4 yards) in 2017.
Robinson recorded 80 receptions for 1,400 yards and a league-leading 14 touchdowns during his Pro Bowl season in 2015. The 6-foot-3, 225-pound Robinson then led the Jaguars in catches (73), receiving yards (883) and receiving touchdowns (six) in 2016.
Robinson has totaled 202 career catches for 2,848 yards and 22 touchdowns since being selected by Jacksonville in the second round of the 2014 NFL Draft.
Quarterback Blake Bortles spread the wealth this past season for Jacksonville by throwing to wide receivers Marqise Lee, Allen Hurns and rookies Keelan Cole and Dede Westbrook.
Chicago's passing game struggled mightily with Kendall Wright leading the team in receptions (59) and receiving yards (614). Backup tight end Adam Shaheen, who had 12 catches, led the team with three receiving scores.