The Bengals officially announced the deal Monday but did not disclose details. A league source told ESPN NFL Insider Adam Schefter that Atkins agreed to a five-year deal worth $55 million.
The Bengals referred to the deal as a "long-term contract extension" on their official Twitter account:
— Cincinnati Bengals (@Bengals) September 2, 2013
Atkins said he appreciated the faith that the Bengals demonstrated by agreeing to the extension.
"It means a lot. Just that they believed in me," he said. "That's basically going to show the younger guys that if you do the right things on and off the field that you're going to be rewarded, too."
Atkins, a former fourth-round draft selection who was scheduled to earn $1.4 million under the last year of his rookie contract, will make $22 million in the first six months of his new deal.
"Everybody sees it. ... I don't have to hold him up, everybody sees it," Bengals coach Marvin Lewis said. "More than anything, it doesn't matter how you get here, what rounds -- fourth, fifth, sixth, college free agent or whatever. If you do things the correct way, you're going to have opportunity."
The contract will pay Atkins $36 million in new money over the first three years of the extension, the source told Schefter.
Atkins emphasized that he was relieved to have the deal completed prior to the start of the regular season.
"It was important because I don't have that weighing on my head or any distractions," he said. "It's not, are we talking midseason or at the end of the season? Now I can just have a clear mind and go out there and try to play fast and hard and just focus on football."
Atkins will make $31 million over the same period that he likely would have made $21 million for playing out this season and being franchised in 2014 and 2015 under very affordable franchise-tag tender amounts. The defensive tackle franchise tender amount for 2013 is $8.45 million.
The 25-year-old Atkins recorded a career-high 12.5 sacks for the Bengals last season, his third in the NFL. The two-time Pro Bowler has 23 sacks in 48 career games.
Cincinnati has spent more than $180 million since the end of last season keeping its team intact. The Bengals have reached the playoffs each of the past two seasons as wild cards, only to lose to the Houston Texans in the first round each time.
Atkins is the 12th Bengals player to get either a new contract or an extension since the end of last season.
"[We're] trying to make sure we re-sign and retain our players and that we continue to move forward with our young guys and keep focus on that and coach them to get better," Lewis said. "Geno has been one of those players since he came here. He's done a tremendous job in being productive on the field."
ESPN NFL Insider Adam Schefter, ESPN.com's Coley Harvey and The Associated Press contributed to this report.