The trade, which cannot become official until free agency opens Tuesday at 4 p.m. ET, will also rely on Marshall passing a physical. The Jets are sending a fifth-round pick to the Bears in return, according to a source.
A nine-year veteran and five-time Pro Bowler, Marshall fought through nagging leg injuries most of last season and finished the year on the injured reserve due to fractured ribs and a punctured lung. He produced just 721 yards receiving. Before last season, Marshall racked up 1,000 yards receiving in seven consecutive seasons.
Although Marshall's ability has never been questioned, he has often been a distraction. Last season, Marshall was part of a postgame locker room rant after a loss to the Miami Dolphins, and he challenged a Detroit Lions fan to a boxing match on Twitter.
In addition, he had weekly television duties as an analyst on Showtime's "Inside the NFL."
A mental health spokesman, the 30-year-old Marshall has seemed to put his past off-the-field issues in the rearview mirror. The mercurial receiver will join a Jets team that figures to rely on young quarterback Geno Smith and currently has receivers Percy Harvin and Eric Decker under contract, although Harvin is likely to be released by the team.
Jets first-year head coach Todd Bowles was a key voice in making the trade. He was a member of the Dolphins' coaching staff in 2010 and 2011, Marshall's two-year run with the team. The Jets' new director of college scouting, Rex Hogan, was a longtime Bears scout, so he, too, has familiarity with Marshall. His position coach in Miami, Karl Dorrell, is now the Jets' receivers coach.
In a span of 12 months, the Jets have remade their once-woeful receiving corps. Their starters will be Marshall and Decker, whom they signed last year to a five-year, $36.25 million contract in free agency.
Marshall will count $7.7 million against the Jets' cap -- a $7.5 million base salary, which becomes guaranteed Thursday, plus a $200,000 workout bonus. They can save $10.5 million by releasing Harvin. If they do so by March 19, they will owe a sixth-round pick to the Seattle Seahawks, per last October's trade agreement. If he's on the roster, the pick escalates to a fourth-rounder.
The move is the first major splash made by Chicago's new leadership regime. The Bears hired coach John Fox and general manager Ryan Pace this offseason to succeed Marc Trestman and Phil Emery, respectively.
Marshall's wife, Michi, took to Instagram to thank the city of Chicago.
The Marshall trade will save the Bears $7.7 million in cash with the trade while creating $3.95 million in cap space. But the club will be saddled with $5.625 million in dead money on the 2015 cap.
While the Bears have elected to move Marshall, the team plans to re-sign backup quarterback Jimmy Clausen, a source told Schefter. The decision to re-sign Clausen comes at a time where the new Bears brass has remained noncommittal about the future of incumbent starter Jay Cutler, who is in the midst of a seven-year, $126.7 million deal. If Cutler is still on the Bears' roster on Thursday, $10 million of his 2016 salary becomes guaranteed.
Information from ESPN.com's Michael C. Wright and Rich Cimini contributed to this report.