Johnson's private workout was viewed by Diamondbacks coaches on a field away from the media. Johnson said he wasn't trying to keep the workout a secret.
"Just in case I'm launching balls over in the White Sox' parking lot," Johnson said with a chuckle, referring to the Diamondbacks' spring training neighbors. "I was going to report to you guys regardless."
Johnson, who waived his no-trade clause to accept the deal, was acquired for right-handed reliever Luis Vizcaino and three minor leaguers: right-handers Ross Ohlendorf and Steven Jackson, and shortstop Alberto Gonzalez.
"I'm feeling a lot better than I did the last time I picked up a ball, let's put it that way," said the 43-year-old left-hander, who rejoined the Diamondbacks following two turbulent seasons with the New York Yankees.
"For the first step, off the mound today, I felt very pleased and I think I'm heading in the right direction," Johnson said. "I'm very happy about that."
If his back responds well, Johnson said he expects to return to the mound on Monday, increasing his pitch count to 30 or 35. Johnson wouldn't set a timetable for pitching in an exhibition game.
"I'm not going to go that far," he said. "I'm not Nostradamus."
Johnson said he might be only two weeks behind the rest of the staff if he continues to make progress.
"It's just going to be a gradual thing that we work through," he said. "As we take those appropriate steps, hopefully there will be no setbacks."
As the Diamondbacks try to end a three-year streak of losing seasons, the team hopes Johnson will bolster a strong rotation led by Brandon Webb, the 2006 NL Cy Young Award winner.
Johnson's best seasons came in Arizona, where he was 103-49 in six seasons and won four NL Cy Young Awards before going to the Yankees in a trade he sought in 2005.