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.

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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:

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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.