Financial terms were not disclosed.
The 6'0", 192-pound native of Regina, Sask., was selected as one of the Capitals' three first-round choices in last year's entry draft.
"He brings speed, offense and good defensive play to the organization," said General George McPhee. "He was well coached at the junior level, and we expect that with continued development he will be a solid NHL player for many years."
In 56 games with Red Deer of the Western Hockey League in 2002-03, Gordon, 19, finished with 33 goals, 48 assists, and 81 points, ranking second on the team in all three categories while scoring a team-high four shorthanded goals.
The Capitals also have decided not to meet the contract wishes of veteran defenseman Ken Klee. He is seeking $3 million while, according to the Washington Post, the Capitals have offered $6 million for three years.