Graham, 39, made 86.76 percent of his 204 field-goal attempts over seven years with the Bengals. He played for nine other teams during his pro career.
Graham didn't kick this season after getting cut by Atlanta at the end of training camp.
"One of the great regrets I have in my career is that I didn't realize how good I had it in Cincinnati," Graham said on the Bengals' website. "There was a time I fooled myself into thinking there were other things more important than what they were. I lost grasp of what true reality was. When I look back on it I feel like I could have been there a lot longer if I made different decisions. But think it made me a better person, made me a better professional."
Graham went to the Pro Bowl in 2005 while with the Bengals. In his last Bengals game in the 2009 wild-card game against the New York Jets at Paul Brown Stadium he missed field goals of 28 and 35 yards in a 24-14 loss.
Graham said on the Bengals website that he was tired of living out of a suitcase and wants to become a special teams coach.