Romo underwent minor surgery to have a non-cancerous cyst removed from his back in April. The surgery prevented Romo from participating in offseason workouts other than some light throwing in walk-through practices.
"He feels good. He looks good," Jones said. "He's uniquely out running mountains right now in the West, so he's getting himself physically in shape. He's never thrown a lot in the offseason. This is a time where he rests his arm. I'm confident his weight is right and feel he'll be in shape and let it go."
Romo and team officials had said he wasn't practicing as more of a precaution.
"I feel a lot better," Romo said in May when asked about the surgery. "It was something that was there a little bit, kind of annoying. I'd rather feel 100 percent here. Hopefully I'll be back for minicamp and be ready to go, but we're just being smart now for the next couple of weeks."
But Romo didn't return for minicamp, and the Cowboys let backup quarterback Kyle Orton take snaps with the first-team offense.
Romo, who signed a six-year extension this spring worth $108 million with $55 million guaranteed, will have more influence with the Cowboys' offense in 2013.
He finished the 2012 season third in passing yards (4,903) and passing attempts (648) and sixth in touchdown passes (28).
"I think here going forward, I'll just be more involved in game-planning," Romo told the Racine (Wis.) Journal Times. "There are certain things I really believe can help us that we're going to do some of that. It's a collective group effort, and I think we're all going to go in there and go to work."
He will have to adjust to a new playcaller for the first time since 2007. Offensive coordinator Bill Callahan will call the plays, a job that had been handled by coach Jason Garrett since Romo's first full season as the Cowboys' starting quarterback.
ESPNDallas.com's Todd Archer contributed to this report.