He is the first University of Virginia product to be drafted by the A's since current closer Sean Doolittle, who was taken in the supplemental first round of the 2007 Draft.
The Draft concludes Saturday, with exclusive coverage of Rounds 11-40 beginning on MLB.com at 10 a.m. PT.
Cogswell has hit .294 with a .394 on-base percentage out of the leadoff spot for the Cavaliers this season, making just three errors in 285 chances. He was an All-Star in the Cape Cod League last summer, collecting 28 hits in 33 games for the Harwich Mariners.
The A's drafted another left-handed-hitting middle infielder in the previous round, taking high school shortstop Trace Loehr.
Aaron Leibowitz is an associate reporter for MLB.com.