Graham remains a touchdown-scoring force but didn't offer much after the catch in 2017.
Graham will officially become a free agent on Wednesday at 3 p.m. CT.
Schefter reports the Packers will sign Graham to a three-year deal.
Ian Rapoport of NFL Network reported the team was considering a trade before the deadline, but Pete Carroll shut down any speculation. But he also hauled in 10 touchdown passes for the first time since 2014.
Just last offseason, the Packers went down the veteran tight end route with Martellus Bennett and it was a disaster.
While his 520 receiving yards were his fewest since his rookie season, he also had 10 touchdowns to rank second in the National Football League behind DeAndre Hopkins.
Two years ago, Green Bay added Jared Cook, who provided a spark in the postseason but was average at best when present on the field during the regular season.
They've got some big questions at the tight end position.
Graham was one of the Saints' best offensive weapons during his tenure in New Orleans, but it took the Seahawks two years to figure out how to take advantage of Graham's skill set as a dominant red zone threat.
As Ralph Mancini pointed out in his post, Graham has been inconsistent. He saw significantly less playing time than Graham or Willson, but still doubled his production from his rookie season to finish with 12 catches for 124 yards and one touchdown.
Green Bay should focus on spending money on the defense and fill the tight end void via the draft.
Graham, 31, spent the past three seasons with the Seahawks, where he was second on the team in targets and receptions last season. But the tight end played just seven games before he was released due to concerns about a shoulder injury the Packers say he didn't disclose.