Strom, 73, had served as the Houston Astros' pitching coach since 2014 before saying he was leaving the team following its World Series run last season.
He told the Chronicle that he wanted to "start new again" in Arizona.
"I was home for, like, two or three days and got the itch again," Strom said. "People that have been in baseball a long time really never lose that feel. When the Diamondbacks did call, it was exciting."
Strom will look to rehabilitate a Diamondbacks pitching staff that had the worst ERA (5.11) in the National League last season and the second-worst in the majors, ahead of only the Baltimore Orioles.
Under Strom, the Astros ranked seventh in the majors in ERA at 3.76. Longtime minor league pitching instructor Bill Murphy will be Houston's pitching coach next season.
Strom pitched for five seasons in the majors from 1972 to 1977, posting a 22-39 record and 3.95 ERA in 100 appearances and 75 starts.