The three-year deal is worth a total of $18 million, a league source confirmed.
Williams, 30, is expected to fly to Seattle on Tuesday and sign -- deals cannot be made official until free agency officially opens at 4 p.m. ET Tuesday.
Williams is ultimately swapping places with cornerback Byron Maxwell, who is expected to sign with the Eagles on a six-year deal worth $63 million that includes $25 million guaranteed, according to sources.
Williams started all 33 regular-season and playoff games during his two seasons with the Eagles. He was part of a secondary that allowed the most passing yards in the NFL in 2013 and the second-most in 2014.
Williams spent an eventful two seasons with the Eagles. Signed as a free agent in 2013 after four years with the Baltimore Ravens, Williams first attracted attention for missing most of the offseason workouts that year. Williams explained that he was spending time with his family and building a new house. Having just won a Super Bowl with the Ravens, he said he needed some time away from football.
During training camp that summer, Williams got into a fistfight with New England Patriots wide receiver Aaron Dobson during a joint practice session. Due to an agreement between head coaches Chip Kelly and Bill Belichick, both players were kicked out of the practice.
Later that summer, Williams' volatile personality surfaced again. He was involved in a practice fight with wide receiver Riley Cooper. Earlier in camp, Cooper was sent home for a few days after an Internet video surfaced showing him shouting a racial epithet during a Kenny Chesney concert.
Information from ESPN NFL Insiders Adam Caplan and Adam Schefter, and Eagles reporter Phil Sheridan contributed to this report.