Green Bay reportedly agreed to terms on a three-year contract with Graham, multiple media outlets reported Tuesday. The contract cannot be finalized until the new league year opens on Wednesday at 4 p.m. ET.
The Packers announced the release of the 32-year-old Nelson, who is coming off his least productive season since 2009, his second year in the NFL. He tumbled to 53 receptions for 482 yards in 2017 after amassing 97 catches for 1,257 yards and 14 TDs in 2016.
Graham, 31, re-emerged as a scoring threat last season with Seattle, hauling in 10 touchdown passes. The 6-foot-7, 260-pound Graham had 170 catches in his three seasons with Seattle.
Earlier Tuesday, ESPN reported that talks had stalled between Graham and the New Orleans Saints, with whom he played his first five seasons and reeled in 51 touchdown catches.
It marks the third straight year the Packers targeted a tight end in the offseason. They signed Jared Cook in 2016 and brought in Martellus Bennett as a free agent a year ago.
Nelson burst into stardom in his fourth season with Green Bay, piling up 95 catches for 1,263 yards and 15 touchdowns in 2011. He set career highs with 98 receptions and 1,519 yards and added 13 TD catches in 2014 before a knee injury cost him the entire 2015 season.
He bounced back to lead the league with 14 touchdown catches in 2016, but failed to reach 80 receiving yards in any game last season and was limited to 35 yards or fewer in his last nine games. Nelson was scheduled to make $9.25 million in 2018.
"He has been an exemplary professional and teammate and greatly contributed to our success," Packers general manager Brian Gutekunst said in a statement. "Jordy will always be a member of the Packers family and we look forward to his eventual induction into the Packers Hall of Fame."