Arbitrator Stephen Burbank has made the decision, despite Graham lining up either in the slot or out wide on over two-thirds of his snaps during last season.
Graham argued that with that being the case, he was entitled to be paid as a wide receiver, meaning an extra $5m (£2.9m) annually from the Saints under the league's franchise-tag rules.
However, Burbank has sided with Graham's team and the NFL Management Council, who jointly argued that the tight end position has always involved a combination of splitting out wide to run pass routes and staying in to block.
The 27-year-old can appeal the decision alongside the NFL Players Association. If he goes ahead with an appeal, it must be submitted within 10 days, before a three-member panel.
In a statement, the NFLPA said: "We will review with Jimmy Graham the decision from Arbitrator Stephen Burbank which permits the player to be designated as a tight end for franchise tag purposes.
"We will advise Graham of his options and carefully determine next steps in this matter. We will also continue to assist Graham and his representation as necessary to help the player reach a fair long-term deal with the New Orleans Saints."
The deadline for signing long-term deals with franchised players is July 15.
Graham has 36 touchdown catches to his name over the past three years - more than any other player in the NFL. Over that time, he has averaged 90 receptions, 1,169 yards and 12 touchdowns per season.