The Nationals outrighted Krook to Triple-A Rochester on Tuesday, but he rejected that assignment and declared free agency.
The 31-year-old was designated for assignment by Washington over the weekend, and he'll hit the open market after passing through waivers unclaimed. In eight appearances between the Athletics and Nationals this season, Krook has surrendered nine earned runs with a 7:6 K:BB across 6.1 innings.