Clark was moved for a 2019 first-round pick and a 2020 second-round pick, sources told ESPN's Adam Schefter.
The two clubs will also swap 2019 third-rounders. Kansas City holds two second-round selections in next year's draft and the lower of the two slots will be given to Seattle.
Soon after the trade, Clark and the Chiefs agreed on a five-year, $105.5-million contract that includes $63.5 million guaranteed, Schefter added. The deal surpasses DeMarcus Lawrence's recent extension with the Dallas Cowboys and sits second behind Khalil Mack in terms of average annual value among edge rushers.
The star defender was slapped with the franchise tag and reportedly didn't intend to show up for training camp without a new long-term contract.
The Seahawks now possess two first-round picks in Thursday's draft: No. 21 and No. 29 overall.
Clark is a significant addition to a Chiefs pass rush that lost Dee Ford in a trade with the San Francisco 49ers this offseason. He'll presumably slide in opposite newly acquired defensive end Emmanuel Ogbah or Alex Okafor in the starting lineup.
A second-round selection in 2015, Clark established has himself as one of the league's top pass-rushers with 22 sacks over the past two seasons.
Seattle, meanwhile, is parting ways with one of its top defenders, who may have been deemed expendable after the team signed quarterback Russell Wilson to a lucrative contract extension. The Seahawks could target Clark's replacement with one of their first-day selections.