The Saints and Graham came to terms on a long-term deal to make the 27-year-old the best-paid tight end in the history of the NFL.
This followed an off-season battle between the parties as to how Graham should be paid as he believed that he deserved wide-receiver money, which the Saints rebuffed. However, Graham has now signed his deal and is glad the situation has been resolved.
"I'm beyond excited," he told the team's official website. "I didn't get into to football to learn litigation.
"I got into football to win games with my teammates, friends and coaches. I am extremely happy to get back to what it's really about."
Graham recorded 86 receptions for 1,215 yards along with 16 touchdowns last season.