"It feels good," Jones said after practice Tuesday. "I can put this behind me and just do what I do now. I just want to first off thank God for this blessing and thank this whole organization. They said they were going to do it. It just proves how much these guys trust and believe in me as a player, but more importantly as a person on and off the field."
Jones said the two sides had been working on a new deal since OTAs in the spring.
The safety admitted it wasn't easy going through training camp while looking for a long-term contract.
"It's kind of hard, but once you trust in those guys ... I trusted them. Like Jeff (Ireland) said, just trust in me, continue to go out and do what I do and everything will work out for you.
"I can put this in the back of my mind and go out and just continue to play football, do what I do, now."
Jones' new deal will put him among the highest-paid safeties in the league. Pittsburgh's Troy Polamalu has the highest base salary among safeties in 2013, according to spotrac.com, with a reported $7.5 million.
But Jones doesn't buy the notion that the new contract will increase pressure on him. In fact, he's thinking the opposite.
"It takes the pressure off," Jones said. "I know where my home is for the next couple of years. The sky's the limit. I can put this behind me, this contract talk, and go out and play football."
Jones is coming off an impressive 2012 season that earned him some Pro Bowl chatter, even though he ultimately wasn't selected to the all-star game.
He was ranked third among NFL safeties by profootballfocus.com behind only Eric Weddle of the San Diego Chargers and Jairus Byrd of the Buffalo Bills.
Jones ended up with 94 tackles, four interceptions, two fumble recoveries and two forced fumbles last season, but he hopes even better things will come in 2013.
"The sky's the limit," he said. "I think I went out last year and demonstrated that I was one of the elite safeties in the game. I just want to be consistent, continue to do what I'm doing and be a leader on this team."
As for celebrating the new contract or buying something extravagant, Jones said now is not the time.
What he did have time for was calling his grandmother.
"I just called my grandma and told her everything's good," he said. "I just want to focus on football now and help this team win some championships."