They waited until just about the last minute, but All-Pro tight end Jimmy Graham agreed to terms Tuesday on a new contract that will keep him in New Orleans for the long haul.

The terms of the contract have not been disclosed, but Greg Bensel, the Saints’ senior VP of communications, confirmed shortly after Graham’s tweet that it is a multiyear deal.

UPDATE (9:50 a.m.): ESPN’s Adam Schefter reports, citing a league source, that Graham’s deal will make him the NFL’s highest-paid tight end. The details:

Graham was among the NFL’s most effective pass-catchers last season, leading the league with 16 touchdown receptions and pacing all tight ends with 86 catches for 1,215 yards.

This production sparked an argument over whether the 27-year-old should be considered a tight end or a wide receiver in terms of the league’s franchise-tag regulations, with an arbitrator eventually ruling that he is, indeed, a tight end. Now that Graham has agreed to a new contract, however, that debate becomes moot.

Under NFL rules, Graham and the team had until 4 p.m. Tuesday to come to terms on a long-term deal.