Graham has been one of the most prolific tight ends of his era, catching 69 touchdown passes since he entered the league with the New Orleans Saints as a third-round pick in 2010. That total ranks second among tight ends and third among all pass-catchers during that span, behind Rob Gronkowski (76) and Dez Bryant (73).
Cutting Nelson, 32, will give the team more than $10.2 million in cap space.
The Packers were in the market for a tight end after the Martellus Bennett signing from last offseason blew up on them.
After negotiations broke down with Jared Cook, the Packers turned to Bennett. He signed a three-year, $21 million deal but played in only seven games before he was waived with the designation that he failed to disclose a medical condition (shoulder) in what proved to be an ugly divorce.
He was claimed off waivers by the Patriots and played in two more games before he went on injured reserve. The Packers are still trying to recoup part of Bennett’s $6.3 million signing bonus; they lost a grievance but have filed an appeal.
Packers tight ends combined for only two touchdown catches last season – tied for the fewest in the NFL. Lance Kendricks, who was signed the day after Bennett, caught one.
Richard Rodgers, who will be a free agent, caught the other. The Packers and quarterback Aaron Rodgers have operated best with a receiving tight end, dating to Jermichael Finley and including Cook. Graham caught 10 touchdowns last season, most among tight ends last season and tied for second-most in the NFL regardless of position.
Graham’s three seasons with the Seattle Seahawks were a mixed bag. In 2017, he caught 10 touchdown passes – all in the red zone – and last season ranked tops among tight ends and tied for second-most among all pass-catchers for receiving scores.
Packers tight ends combined for two receiving touchdowns last season, tied for fewest in the NFL.
Outside of his touchdowns, however, Graham suffered a decline in his production. His 520 receiving yards represented a significant drop-off from 2016, when he had 923 receiving yards. And dropped passes were also an issue as Graham tied for the second-most in the NFL with seven in 2017, according to ESPN Stats and Information.
Graham’s lack of production outside of the red zone in 2017 led many to suspect he has lost a step due to a combination of age — he turns 32 in November — and the major knee injury that cut his first season in Seattle short.
He suffered a torn patellar tendon in November 2015, causing him to miss the final five games for Seattle, though he didn’t miss a game over the next two seasons.
The Seahawks acquired Graham and a fourth-round pick in a trade with New Orleans in 2015, sending center Max Unger and a first-round pick to the Saints.
Graham’s last contract, signed with New Orleans in 2014, was for $40 million over four years. No tight end since then has topped that deal on a per-year-average basis.
ESPN’s Brady Henderson contributed to this report.