Diamondbacks manager Torey Lovullo announced his decision to reporters Tuesday.
Boxberger, who was traded to Arizona by Tampa Bay last November, was an All-Star closer for the Rays in 2015 but has been limited by injuries over the last two seasons. The right-hander, who led the American League with 41 saves in 2015, went 4-4 with a 3.38 ERA in 30 appearances last year for the Rays.
The hard-throwing Bradley emerged as one of baseball's top relievers last season, when he posted a 1.73 ERA and had 79 strikeouts in 73 innings over 63 appearances. Lovullo cited Bradley's versatility as a reason behind the decision to keep the former starter in a more flexible relief role.
"Archie's versatility, being able to have him for two, three, four or five [outs] at any time, was very important to the success of this team last year, and we wanted that to continue," Lovullo told reporters, according to AZCentral.com.
Japanese right-hander Yoshihisa Hirano, who signed a two-year, $6 million deal with the Diamondbacks in December, also had been a candidate for the closer role. Lovullo told reporters that he plans to start the season with Hirano in a setup role pitching the seventh or eighth inning.