To clear space on the 40-man roster, the club transferred right-hander Jesse Hahn to the 60-day disabled list, recalled right-hander A.J. Griffin from Nashville and placed him on the 60-day DL (strained right shoulder) and outrighted Angel Castro to Nashville.
Blair and Dull will both be making their Major League debuts.
Blair was a non-roster invitee with the A's this spring who has hit .252 with nine home runs and 37 RBIs in 88 Minor League games this year.
Between stints with Double-A Midland and Nashville, Dull is 3-2 with 12 saves and a 0.74 ERA in 47 relief appearances.