Webb will pitch the first game in Tucson, Ariz., while the second game takes place at Chase Field, the home of the D-backs.
Webb, who is a free agent after the season, hasn't pitched in a game in nearly two seasons because of shoulder problems.
It was learned by MLB.com on Friday that he would have interest in playing for the Nationals if he doesn't re-sign with the D-backs. It's not a secret that Webb has a close relationship with general manager Mike Rizzo, who drafted Webb in the 2000 First-Year Player Draft when Rizzo was director of scouting with Arizona.
According to published reports, Webb threw one inning on Wednesday and didn't have any problems throwing the baseball. He told MLB.com that day that his fastball was clocked in the 80s, but he expects the velocity to improve with each outing.
It was the first time Webb faced hitters in a game since Opening Day 2009, when he experienced shoulder discomfort that would lead to shoulder surgery in August of that year.
If he signs with any team, Webb most likely would have to sign an incentive-laden deal given his long period of inactivity.
Rizzo was not available for comment.
Webb may be a risk worth taking. There was a three-year period where Webb was arguably the best pitcher in baseball. In 2006, he won the National League Cy Young Award by going 16-8 with a 3.10 ERA. Two years later, he won 22 games and had a 3.30 ERA with the D-backs.