Plumlee's contract is for four years and $6.5 million, a source said.
"They're very good about that. I think I was one of the first [rookies] to sign," Plumlee said. "[They] got everything worked out and it was very easy."
The Nets took the Duke big man with the 22nd overall selection in the NBA draft.
"I had a hard time sleeping last night," Plumlee said Wednesday, after participating in his first summer league practice under first-year coach Jason Kidd. "You dream about this. [This] is where you want to be as a player, so it was a little tough getting to bed. But I thought the first practice was OK, and I'm looking forward to coming back tonight [for the second session]."
Plumlee was asked what it was like playing for Kidd as opposed to Mike Krzyzewski, who has been Duke's head coach for 33 years.
"Everybody's gonna keep asking me that," Plumlee said, laughing. "They're both great basketball minds. We'll see. Coach K turns it on once you lose, so we'll see.
"[Kidd] knows what he's talking about. Everyone's going to listen to him like he's been coaching for 20 years. He coached a lot of those games [he played in] with his jersey on.
"He did a great job [Wednesday]. Everything he says is right on, so I don't think it's going to be much of a transition for me."
Asked what practice was like, Plumlee said, "A lot of it was walking through, just where to be and when, just different terminologies. A lot of it was just picking up that stuff."
Plumlee says he can bring athleticism, strong rebounding and inside scoring to the Nets. He will wear No. 1 for the Nets this season.