Matusz, 30, was the fourth overall pick in the 2008 Draft by the Orioles. The left-hander appeared in seven games for the O's last season and one for the Cubs. In parts of eight seasons in the big leagues, Matusz has a 4.92 ERA in 280 games (69 starts).
Initially a starter, Matusz has mainly pitched out of the bullpen since 2013, posting a career 3.47 ERA in relief. The D-backs only have two lefty relievers on their 40-man roster with any big league experience in Andrew Chafin and Steve Hathaway.
Jepsen, 32, made a combined 58 relief appearances for the Twins and Rays last year, compiling a 5.