Jones played two games in a short injury rehab with Class A Rome. His last test was performing running drills before batting practice on Monday under the supervision of trainer Jeff Porter.
"The biggest thing that was causing me pain until this weekend was hitting right-handed," said the switch-hitting third baseman.
Jones said he has no continued concern about his right-handed swing.
"I assured them there will be nothing knee-related that will keep me out of there," Jones said, adding he had some soreness in other parts of his legs as he returns to playing shape.
To make room for Jones, outfielder Wilkin Ramirez was optioned to Triple-A Gwinnett.
The Braves waited until after batting practice on Monday to send Ramirez back to Gwinnett after considering a move to place outfielder Jordan Schafer on the disabled list. Schafer has been unable to swing a bat due to what has been called a jammed left middle finger. He said he had X-rays early Monday which showed a chip fracture in the finger.
Schafer said he believes he'll be ready to start in a couple days.
The 39-year-old Jones had arthroscopic surgery on July 9 to repair torn cartilage in the right knee.
Manager Fredi Gonzalez said he'll use a pinch-runner for Jones late in games but trusts that the veteran has full clearance.
"I trust him. We trust him," Gonzalez said. "He knows his body. He's good."