Walker, the penultimate selection of the third round, played last season for Washington's primary developmental team, the Hershey Bears, and scored five goals in 43 games.
The 25-year-old left wing was ineligible to be selected last year because he played early in the year in the Czech Republic, but now has a full season of experience in the level just below the NHL.
Walker attended the Capitals training camp last season and played some pre-season games for the club, scouts praising his speed and work ethic.
Walker was born in Cardiff, Wales, but grew up in Australia. His family moved to Sydney and he played rugby league as well as ice hockey before moving to the Czech Republic in 2007 to boost his hockey skills.