Graham had been planned to go home to Dublin, Va., after being waived himself by the Carolina Panthers, and had his bags packed just in case.
"I packed one of my suitcases for a week of clothes because I had a feeling I was going to get a call," Graham said. ""I also took all my kicking stuff. I wanted to get back and see my family for at least a day, but I was confident I had done enough that somebody was going to pick me up pretty soon."
Graham, 25, will be the Bengals' fifth Opening Day placekicker in the past 23 years. The others were Jim Breech, Jim Gallery, Doug Pelfrey, and Rackers.
Graham drove from Charlotte to Cincinnati on Monday in six-and-a-half hours.
With Carolina, Graham, an undrafted free agent out of Virginia Tech in 2000, lost the battle to unseat incumbent John Kasay.
Rackers had been with Cincinnati for three years.