The contract has a base salary of $925,000 with maximum rookie contract signing bonuses giving him a salary-cap number of $3.225 million, the team said on its website.
"This is one of the best days of my life and career, so far," Jones said. "Hopefully there are a lot of good days to come, but this is surreal still. I am very happy to be here right now."
Jones, 18, was selected with the No. 4 pick and has been attending Predators development camp this week.
"I'm excited to be one step closer to realizing the dream of playing in the NHL, especially with a world-class organization like the Nashville Predators," Jones said. "Since being drafted by the Predators and coming to development camp, I'm certain this is the right spot and right organization for me. I can't wait for the opportunity to learn from and play with world-class players like Shea Weber and Pekka Rinne and other veteran players who will help me in my development on and off the ice."
General manager David Poile, who was thrilled to find Jones (6-foot-4, 205) still available after the Colorado Avalanche, Florida Panthers and Tampa Bay Lightning made their selections, is just as happy to have Jones under contract.
"Seth is a special prospect and we were fortunate to be in position to select him," Poile said. "As a player, he brings so much to our organization, from size you can't teach to a skill set that every team hopes to add and a personality and maturity that will allow him to grow and develop with our veteran core and other young players. He has excelled at the junior and international levels and we anticipate him enjoying great success at the NHL level."
Jones' father, former NBA player Popeye Jones, was on hand Wednesday.
"As I have said to Seth and his dad, very good parenting," Poile said. "They have done a very good job. Good parenting and good mentors along the way, and we’re very proud to have Seth as a player and a person joining our organization."