Arizona also designated right-hander Esmerling Vasquez for assignment.
Zagurski had a 5.40 ERA with four strikeouts in four games with the Phillies this season. He also went 4-0 with 11 saves and a 2.65 ERA in 46 games with Triple-A Lehigh Valley.
The 28-year-old has played parts of three seasons in the majors with the Phillies, going 1-0 with a 6.82 ERA in 37 games.
Vasquez went 1-1 with a 4.15 ERA in 31 games during two separate stints with the Diamondbacks this season.