Graham skipped all of the Saints' voluntary and mandatory practices and workouts - and challenged the NFL's franchise tag process through arbitration.
The odds of Graham leaving the Saints were slim since the club in late February placed its franchise tag on the player.
The NFL Players Association filed a grievance, contending Graham was used as a wide receiver often enough to qualify for the more lucrative receiver tag, worth about $5 million a year more than the $7 million tag for a tight end.
A hearing was held in June and earlier this month. Arbitrator Stephen Burbank sided with the NFL, ruling Graham was capable of continuing to perform specific tight end duties while lined up in the slot or within 4 yards of an offensive tackle.
Once the ruling was in place, Graham had a choice of appealing or trying to reach a long-term contract by a July 15 deadline - after which he would have to play next season for his franchise tag number. A favorable ruling from Burbank would have further enhanced negotiating leverage for Graham, who last season led the Saints with 86 catches for 1,215 yards and 16 touchdowns.
Graham, a former college basketball player who played one year of football at Miami, was the Saints' third-round draft choice in 2010. In his second season, Graham caught 99 passes for 1,310 yards. That total stood briefly as a yards receiving record for tight ends. That same day the mark was broken on the final day of that season by New England's Rob Gronkowski, who finished with 1,327.
Graham has led the Saints in catches the past three seasons and led them in yards receiving and touchdowns in two of the last three seasons. For the past three regular seasons, he has 270 catches for 3,507 yards and 36 touchdowns.