The Jets also get Seattle's 2018 second-round draft pick, and the teams swapped seventh-round picks.
Kearse, 27, has been a starter for the Seahawks since 2014 but is coming off a down season in which he caught 41 passes for 510 yards and one touchdown. He was briefly supplanted as Seattle's No. 2 receiver behind Doug Baldwin, but he reclaimed that role when Tyler Lockett suffered a season-ending leg injury in December.
Richardson, 26, has spent his entire four-year career with the Jets. The former Defensive Rookie of the Year made the Pro Bowl in 2014.
"Another team wanted me," Richardson told ESPN's Josina Anderson. "Got to roll with the punches. I'm happy for the situation I'm in now. Fresh start.
"I can't wait to contribute on a defense with guys like that. I want to get out there and start on defense. That's the plan."
"We obviously think very highly of Sheldon," Jets general manager Mike Maccagnan said in a conference call with reporters. "We were positive with him, but we thought [the trade] was a good fit and a good value for what we're trying to accomplish, both short and long term."
Maccagnan wouldn't say if the team approached Richardson about a long-term contract extension. A source told ESPN's Rich Cimini the Jets showed no interest in re-signing Richardson beyond this season. The Seahawks are picking up his $8.1 million salary for this season.
Maccagnan said he believes a surplus of talent on the defensive line allowed the Jets to make the trade.
"We have some good, young defensive linemen," Maccagnan said. "Sheldon was part of that, but in return, it allowed us to entertain options. Short term and long term, we're still committed to building this thing through the draft. It was an opportunity to acquire some draft capital and also acquire an element to our team, not just from a talent standpoint, but from a character and intangible standpoint in the receiver room."
Richardson's immaturity has been a concern to some people in the organization. He has been suspended twice by the league, and he recently angered Todd Bowles with his public criticism of former teammate Brandon Marshall.
Seahawks owner Paul Allen expressed his regards for Kearse via Twitter.
— Paul Allen (@PaulGAllen) September 1, 2017
Kearse is set to make $2.2 million in base salary in 2017 as part of the three-year, $13.5 million deal he signed in March 2016.
The acquisition of Richardson strengthens what was already one of the NFL's better front sevens, and it gives the Seahawks the interior pass-rusher they thought they were getting with top pick Malik McDowell, who might miss his rookie season following an ATV accident.
A significant move like this seemed to be in the offing when the Seahawks cleared $5.2 million in salary-cap space for 2017 by restructuring Baldwin's contract, which was reported by ESPN's Field Yates.
It marks the fourth time the Seahawks have traded for a star player under general manager John Schneider and coach Pete Carroll, who previously made deals to acquire running back Marshawn Lynch in 2010, wide receiver Percy Harvin in 2013 and tight end Jimmy Graham in 2015.
Richardson told Anderson that he is flying to Seattle on Friday night.
Information from ESPN's Brady Henderson and Rich Cimini was used in this report.