Klobosits was claimed off waivers by the Athletics on Monday, Martin Gallegos of MLB.com reports.
Klobosits was designated for assignment by the Nationals on Wednesday after posting a 5.56 ERA and 5:5 K:BB in 11.1 innings as a rookie last year. Luis Barrera was designated for assignment to clear space on the 40-man roster. Klobosits is expected to report to Triple-A Las Vegas.