The 24-year-old defenseman, who has been working with the second power-play unit in practice, was activated from injured reserve Monday. He missed four weeks with a Grade 2 MCL sprain sustained during the Kraft Hockeyville USA preseason game against the Buffalo Sabres in Clinton, New York, on Sept. 25.
"I don't know how much happier I can be to be back," said Jones, who will wear a brace on his right knee. "The confidence is back. The first couple of times you're skating on it, you're not too confident on it, you're not too sure what to think of the brace and all that fun stuff that goes with it. But my speed is there. I think my quickness is there, my agility. The past couple of days I've started to battle a little bit more down low and try to get that feeling back. It's been good."
Jones was expected to need 4-6 weeks to recover.
"Oh I'm sure. I could see it just on the ice today when we were moving the puck around," coach John Tortorella said after practice when asked about whether Jones would be rusty. "He's been out for a while. That's going to come pretty quickly though. That's a really good athlete that we're dealing with here."
Jones had 57 points (16 goals, 41 assists) last season, a single-season record for a Blue Jackets defenseman, and finished fourth in voting for the Norris Trophy.
Selected by the Nashville Predators with the No. 4 pick in the 2013 NHL Draft, Jones has 182 points (45 goals, 137 assists) in 393 games with the Predators and Blue Jackets.
Forward Alex Galchenyuk will make his season debut for the Coyotes. Galchenyuk, acquired by Arizona from the Montreal Canadiens on June 15 in a trade for forward Max Domi, hasn't played since the preseason because of a lower-body injury.