He was simply phenomenal, but he has struggled in recent years, posting an average of just 50 catches and 534 yards over the past three seasons.
However, Graham is now determined to disprove any notions that he's taken a big step backward.
"I'm still fast. ... I still have the ability to make big plays," he said in a conference call with reporters Thursday (h/t ESPN's Jeff Dickerson).
The Green Bay Packers released Graham after two seasons, and the Bears soon signed him to a two-year, $16 million deal with $9 million guaranteed. As Dickerson noted, that contract was "arguably the most universally panned move in free agency."
But Graham said Thursday that the Packers release "lit a fire" under him before noting the following:
"I know what player I am and I know what I can do. I think I was able to show a little bit of that in the playoffs with some of the opportunities I was given. And after being 10 years in, I've only missed six games. That's coming off of, at times, all kinds of injuries... at times I've kind of been on ice the last two years so my knee right now is the best it's felt in four or five years.
"This is the best that I've ran, this is the fastest I've been in the last four or five years. I'm going to get back to being me, I'm going to get back to making big plays and scoring touchdowns because I think I'm somewhere in the top of scoring touchdowns and I want to continue that, I want to continue climbing that list and get to where I'm supposed to be."
The 33-year-old will be entering his 11th NFL season.
The Bears are hoping Graham can provide some stability to a tight end position that hasn't seen any since Martellus Bennett left after the 2015 season.
Chicago used a handful of players at the position in 2019: Trey Burton, Jesper Horsted, J.P. Holtz, Ben Braunecker and Adam Shaheen.
Burton, who excelled as a member of the Super Bowl LII champion Philadelphia Eagles, was brought in to be the team's starter in 2018, but a groin injury limited him to just eight games in 2019 and curtailed his production when on the field.
Graham is now atop the depth chart, however, and the Bears are hoping he returns closer to the form exhibited earlier in his career.