He said he'll join the D-backs' Triple-A affiliate in Reno, Nevada, in Las Vegas on Tuesday.
"I'm excited," Harrell told MLB.com "It's a new opportunity. It's a fresh start, a chance to go out there and work on some of the things I wasn't doing well, which was causing me to be unsuccessful with the Astros. Hopefully I'll get it all corrected and make it back to the big leagues."
Harrell's stock had fallen significantly since his breakout 2012 campaign, in which he was 11-11 with a 3.76 ERA in 32 starts. He's at this best when he has his sinker working and is working at a quick tempo, and had flashes last season that were reminiscent of the 2012 Harrell. He allowed two or fewer runs in 11 of his 22 starts, and finished seventh in the American League with a 1.93 ground-ball-to-fly-ball ratio.
Harrell had a solid April in 2013 before having a rough stretch in May, in which he went 1-4 with a 7.53 ERA in six starts. By July, he was out of the rotation and sent to the bullpen.
"I had a good year and a half," Harrell said. "The first part of last year was pretty good, and then I struggled. I kind of got what I deserved, because if you don't pitch well, you don't get an opportunity to stay."
Claimed off waivers from the White Sox in July 2011, Harrell wound up being the Astros' most effective starting pitcher in 2012 before going 6-17 with a 5.86 ERA in 36 games (22 starts) in 2013.
Harrell on Monday thanked former owner Drayton McLane and former general manager Ed Wade in showing faith in him, and current GM Jeff Luhnow in giving him a chance.
"The fans were great," Harrell said. "Hopefully, [the Astros] will get everything figured out, what they want to figure out, and they can start winning some ballgames for the city. The city will be behind the team if they're winning, and hopefully they can get back to where they were in 2005."
Brian McTaggart is a reporter for MLB.com and writes an MLBlog, Tag's Lines. Follow @brianmctaggart on Twitter. This story was not subject to the approval of Major League Baseball or its clubs.