The Giants selected Kilian's contract from Triple-A Sacramento on Wednesday.
Kilian won a bullpen job as a non-roster invitee after yielding just one run with an 11:2 K:BB over 9.1 innings during Cactus League play. The 28-year-old is likely to operate in middle relief initially, but it wouldn't be a surprise if he pushes for a more high-profile role as part of a Giants bullpen that's in flux.