Curry signed a six-year, $60 million deal that includes $34 million in guarantees, according to a source.
Last year's No. 4 overall pick, running back Darren McFadden, got $26 million guaranteed from Oakland.
Curry, the fourth overall choice in the 2009 NFL draft out of Wake Forest, had missed the first eight days of camp. The linebacker's agreement leaves six first-rounders without contracts.
"I am just as excited to be out here and just to see the emotion from the fans and get back with my team is just an amazing feeling," Curry said.
On his first play, Curry was matched up against tight end Cameron Morrah, and was roasted on a square-in route. One fan sarcastically yelled out, "Welcome to the NFL."
"He wasn't in there with the first group just because he's got so much catching up to do," Mora said. "I don't know at what point we'll make the switch and he'll start running out there with the first defense, but I think it will be pretty soon."
Although he worked out and studied his playbook in nearby Bellevue during the holdout, Curry said he grew anxious and eventually told his agents to speed up the contract negotiations.
Fellow rookie Deon Butler filled Curry in on practice matters during the holdout, and Tatupu also visited, giving him a mini-walkthrough of what the defense was working on. But Tatupu believed Curry would acclimate himself quickly.
"Linebacker, it's not like it's rocket science," Tatupu said with a laugh. "Just hit the man with the ball."
Mora credited general manager Tim Ruskell for working the phones with Curry's representatives late into Friday night.
"This is probably the longest contract we'll ever do, in terms of pages and volume and little nuances to the deal," Ruskell said.
Only top overall pick Matthew Stafford, the quarterback drafted by Detroit, has received a richer guarantee -- $41.7 million -- from this year's draft.
ESPN.com's Mike Sando and John Clayton contributed to this report. Information from The Associated Press was used in this report.