Gustafsson is the son of former Capitals player Bengt Gustafsson.
The younger Gustafsson signed a three-year entry-level contract. He was the 21st overall selection. The 19-year-old took part in Washington's development camp last summer and the rookie camp in September.
The announcement of his contract Thursday comes one day after the Capitals were eliminated from the playoffs with a 6-2 loss to the Pittsburgh Penguins in Game 7 of their second-round Eastern Conference series.