Dawson said he's been eyeing the Cardinals for some time.
Jones would have received $15 million had he remained with the franchise tag.
TEMPE, Ariz. (AP) — The Arizona Cardinals have made the big investment they knew would be required after trading for Chandler Jones a year ago, signing him to a five-year contract.
"Those guys will be missed for sure, in the locker room, even on the field," Jones said, "but as a player just being here one year I really truly trust our front office with our owner and our GM and our head coach that we'll get the guys to take us where we need to be."
"I've got a lot left, man," he said. "I been blessed. I can't lie. God's been showing me tremendous favor, showing me tremendous favor bringing me back here."

"Every interview that I've had since I've been here,Wholesale Jerseys USA, everyone's asked me 'How long are you going to be here? Are you going to be a free agent? Are you going to test the market?'" he said. "It's all over. Today's been a great day."
Jones had 11 sacks last season with the Cardinals,Wholesale Jerseys From China, along with four forced fumbles, two fumble recoveries and 15 tackles for loss. He had 12? sacks for the Patriots in his Pro Bowl season of 2015, making him one of three players with double-digit sacks in each of the past two seasons. The others were Von Miller and Khalil Mack.
At a news conference, Jones was happy to have the matter resolved for the long term.
The Cardinals also confirmed earlier reports they had reached contract agreements with inside linebacker Karlos Dansby on a one-year-contract and kicker Phil Dawson on a two-year deal,Cheap NFL Jerseys Free Shipping. It will be Dansby's third stint with the Cardinals.
"This is a destination that's always been attractive to me," he said.
Dansby, 35, needs one more interception to become the fifth player in NFL history with at least 40 career sacks and 20 career interceptions.
"The sky's the limit for our pass rush," Jones said. "I feel like last year we just scratched the surface and we led the league in sacks. Markus is a tremendous player and he's still learning, and I learn from him, honestly. We learn from each other. Even though we have different body types there's a lot of moves, different techniques to get by offensive tackles that help both of us."
Dansby was a second-round draft pick of Arizona; Larry Fitzgerald was the first. Dansby played for the Cardinals from 2004-09, then returned for a strong 2013 season, earning him a lucrative deal with Cleveland. The 13-year NFL veteran led Cincinnati in tackles last season with 114.
Going into his second season in Arizona,2014 Olympic Team USA #44 Brooks Orpik White Stitched NHL Jersey, with his new contract the 27-year-old Jones expects to assume a bigger leadership role.
"Here in my first year, I was kind of shadowing a little bit. I was trying to feel my way around, especially when I first got here," Jones said. "Now knowing that I'm going to be here, I can change roles a little bit, be a leader, be more vocal. But I feel like I played decent. You can never say you had a perfect season, so there's always room for improvement for sure."
Dawson, 42, spent 14 seasons with Cleveland, setting the franchise record for field goals. He was with San Francisco the past four seasons, making 86 percent of his field goals,China Adidas Hockey Jerseys, including 14 of at least 50 yards. Dawson's arrival ends Chandler Catanzaro's time as kicker. Catanzaro had been Arizona's sometimes inconsistent kicker the past three seasons.
The Cardinals' other outside linebacker, young Markus Golden, led the team with 12 ? sacks.
As for the future, Jones said, "there's always room for improvement. Probably just being more consistent. There are a few games where my pass rush could have been better."
The agreement comes after the Cardinals placed the franchise tag on Jones to prevent him from becoming a free agent.
The Cardinals acquired Jones in a trade with New England before last season, and general manager Steve Keim had said all along that the team would sign the player to a long-term contract. It's worth $82.5 million, with $53 million guaranteed.
Jones will be part of a team that has lost defensive starters tackle Calais Campbell, and safeties Tony Jefferson and D.J. Swearinger to free agency. The Cardinals simply couldn't afford to keep Campbell and Jefferson, who landed big deals elsewhere.