The Brewers took Miller in the 16th round last year, but he did not sign. Last summer he played for the Orleans Firebirds in the Cape Cod League, going 5-1 with a 3.20 ERA.
Oakland took six right-handed pitchers in the first 10 rounds of the Draft, and Miller, at 6-foot-3, is the tallest of the bunch.
The Draft concludes on Saturday, with exclusive coverage of Rounds 11-40 beginning on MLB.com at 10 a.m. PT.
Aaron Leibowitz is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.