The deal was first reported by FoxSports.com.
"Jeremy is a player that we are excited to have on our roster. He is someone I am familiar with as a player," Payton said. "He brings a skill set to the position that I feel will be a tremendous benefit to our offense."
The Saints had been trying since February to acquire the disgruntled New York Giants tight end. First, they offered a second-round pick. Before the draft, they increased the offer to a second- and a fifth-round draft choice, but until a few days before the start of their training camp, the Giants felt he was too valuable to lose.
As Payton and Saints general manager Mickey Loomis did their last few minutes of office work before heading to Jackson, Miss., for Wednesday's start of training camp, they received a call from the Giants saying Shockey was theirs.
"Jeremy brought great energy to the game every time he stepped on the field," Giants team president John Mara said. "He had a close relationship with my father from the time we drafted him, and I had a couple of long conversations with Jeremy this spring and summer. From those conversations, it was apparent to me that a fresh start was the best thing for us and for Jeremy."
Even through the weekend, the Saints had tried to broker a deal for Shockey. On Sunday, they tried to get in the middle of the Jason Taylor trade to see whether there was a way they could make a three-way deal that brought them Shockey, according to multiple sources. Taylor went from the Miami Dolphins to the Washington Redskins for a second-round pick in 2009 and a sixth-rounder in 2010.
Chris Mortensen reported that deal would have still sent Shockey to the Saints, with the Giants obtaining Taylor and the Dolphins still receiving the Saints' second- and fifth-round picks in 2009.
The Giants stalled the discussions because GM Jerry Reese wanted to talk to Taylor -- most likely to gauge his interest in playing beyond 2008 and to discuss restructuring his contract -- before he took the next step with the trade, Mortensen reported. But the Dolphins wouldn't grant permission to the Giants to talk to Taylor because they didn't want Taylor to be in control of any deal.
Shockey, 28, a four-time Pro Bowler, has 371 catches for 4,228 yards and 27 touchdowns in his six-year NFL career. He grew disgruntled with the Giants because he wanted to be more involved with some downfield passing. New York valued his run blocking.
Shockey's agent, Drew Rosenhaus, called last season a difficult one for his client, who was looking for a change of scenery.
"He's been one of the most successful tight ends in NFL history, but now I think he's going to be more prolific in the Saints' offense," Rosenhaus said. "I don't think Jeremy could ask for a better situation."
Giants coach Tom Coughlin called the departing tight end "an outstanding football player who plays the game full-speed and plays the game the way it was meant to be played."
"I wish him the best," the coach added.
Not every member of the Giants' organization was pleased with the deal.
"People talk about how we're a better team without him, but those are the people that don't know football," wide receiver Plaxico Burress said, according to the Newark Star-Ledger. "I hear that and it's like, 'You people are crazy. You've never played a down of football in your life, so what would you even know?' The guy walks on the field and he demands a double-team. Before he even straps it up and goes out to play, he's already made the team better. Him going to New Orleans, he makes them one of the best offenses in the league."
"We have five young kids who are all vying for the position," Coughlin said. "The tight end position will be a very competitive position in training camp."
Payton was an offensive coordinator with the Giants during Shockey's rookie season, when Shockey caught 74 passes for 894 yards.
"I have had a relationship with Coach Payton and I appreciate what he has done as a head coach," Shockey said in a statement released by the Saints. "The Saints have a lot of weapons starting with Drew Brees and I look forward to joining my teammates at training camp. This will be a fun year."
John Clayton is a senior writer for ESPN.com. ESPN NFL reporter Chris Mortensen and The Associated Press contributed to this report.