"The last [two] years have certainly been interesting! A lot of memories, friendships and humbling moments that I will carry with me into the next opportunity," Graham wrote Wednesday on Twitter. "Thank you for the support during our exciting run this year toward that ever so elusive ring."
Graham, who turned 33 in November, was the NFL's highest-paid tight end last season with an average salary of $10 million, according to Spotrac. He was scheduled to take up the second-most salary cap space ($11.67 million) among tight ends in the league next season, trailing only Philadelphia Eagles star Zach Ertz ($12.23 million).
The Packers will save about $8 million in cap space with the release of Graham.
In two seasons with the Packers, Graham scored only five touchdowns. Last season, he tallied 447 receiving yards and three touchdowns on 38 receptions, his lowest total since tallying 31 catches in his rookie season in 2010.
The New Orleans Saints selected Graham in the third round of the 2010 NFL Draft out of Miami. He is the only tight end in league history to have two seasons with 1,200-plus receiving yards and 10-plus receiving scores (2011, 2013).
Graham, a five-time Pro Bowl selection and two-time All-Pro choice, has recorded 649 receptions for 7,883 yards and 74 touchdowns between the Seattle Seahawks, Saints and Packers.