The 20-year-old Walker was selected in the third round of last month's draft. He signed a standard three-year, entry-level contract Friday.
Walker was born in Wales but spent his early childhood in Australia before moving to the Czech Republic.
Walker became the first Aussie in the American Hockey League when he played for the Hershey Bears, the Capitals' AHL affiliate. He had five goals, six assists and 40 penalty minutes in 43 games with Hershey last season.