Jones, 26, will receive $71.25 million over the life of the deal, with $47.5 million guaranteed, sources told ESPN's Chris Mortensen.
"I didn't have any doubt in my mind that we were going to get it done," Jones said. "Whether it was this year or next year, we were going to get a deal done. I want to be a Falcon for the rest of my career, and Mr. Blank let it be known that he wanted me here as well."
The two-time Pro Bowl receiver was in the final year of his contract and set to make $10.176 million for the 2015 season. His new contract follows the five-year, $70 million extensions signed by Dallas Cowboys receiver Dez Bryant and Denver Broncos receiver Demaryius Thomas earlier this summer.
Talks between the Falcons and Jones' camp stalled last week but were "jump-started" Saturday morning, sources said.
"Julio is the type of young man we value, and this contract reflects that," owner Arthur Blank said.
Blank made clear the team's intent to re-sign Jones when he addressed the media during training camp.
"We expect Julio to be a lifer for the Falcons," he said.
The extension is the first step in making that a reality.
Jones, considered one of the most dynamic deep threats in the league, set a franchise record with 1,593 receiving yards on a career-high 104 receptions in 2014 despite missing one game with an oblique injury. Jones also topped the league with 31 catches of 20-plus yards.
For his career, Jones has 278 catches for 4,330 yards and 26 touchdowns. He has scored a touchdown of at least 75 yards in each of his first four NFL seasons.
The Falcons are counting on Jones to be even more of a threat in new offensive coordinator Kyle Shanahan's scheme. Shanahan plans to use Jones at various receiver positions rather than just lining him up in the traditional "X" role.
"Just to be around a guy who is as explosive as he is but who can still break down and cut and attack the football and see the ball ... and his toughness," Shanahan said. "The guy doesn't take a play off. He's physically tough and mentally tough. He's very fun to coach. And he makes you a better coach."
Teammates certainly understand Jones' value.
"To me, he's good at so many things," receiver Roddy White said. "He's able to run. He's big. He's strong. He can run route -- underneath routes, intermediate routes. He can go out there on the outside. He doesn't have really no weaknesses in his game."
Jones was the sixth overall pick in the 2011 NFL draft. The Falcons traded five picks to move up in the first round and select him.
ESPN's James Walker contributed to this report.