Graham signed a reserve/future contract with the Falcons on Monday.
Graham had a solid preseason in Atlanta but was unable to make his way onto the 53-man roster in 2018. The 23-year-old out of Yale will hope a full term in the team's offseason program will lead to his NFL debut next year.
Graham hauled in three of his four targets for 36 yards during Thursday's preseason loss to Miami.
Currently situated no higher than fourth on the Falcons' tight end depth chart, Graham's likelihood of making the 53-man roster to start the season seems remote. With Austin Hooper locked into a starting job -- and both Logan Paulsen and Eric Saubert entrenched in backup roles -- Graham remains a promising candidate to join Atlanta's practice squad in 2018. Given his strong showing in Week 4 of the preseason, however, another team may swoop in to secure the 22-year-old's services for a backup role.