The deal is worth $23 million, a source told ESPN's Jeremy Fowler, confirming a report by the NFL Network.
Reed tweeted to express his enthusiasm about returning to Seattle.
Reed hit free agency after a down season with the Seahawks that began with a six-game suspension for violation of the NFL's personal conduct policy.
The suspension stemmed from an April 2017 domestic violence case in which Reed was accused of assault. He was not charged or arrested, with the city's prosecuting office citing insufficient evidence despite a police recommendation of fourth-degree assault/domestic violence following an investigation.
After a breakout 2018 season in which he tied for the fourth-most sacks (10.5) by a defensive tackle, Reed finished with two in 10 starts in 2019 after returning from his suspension. One came on a strip sack of Jimmy Garoppolo that Jadeveon Clowney returned for a touchdown in Seattle's victory against the San Francisco 49ers on Monday Night Football in Week 10.
Reed, who turned 27 in December, was known more as a run-stuffer than a pass-rusher before his breakout 2018 season. He totaled a combined three sacks in his first two NFL seasons and finished with two in his two seasons at Alabama.
Reed was a second-round pick in 2016 and became a full-time starter in his second season after splitting time with veteran Tony McDaniel as a rookie.
In his four NFL seasons, Reed has 156 tackles with 15.5 sacks, 2 forced fumbles, 2 recoveries and 8 tackles for loss.
ESPN's Brady Henderson contributed to this report.