The 25-year-old forward, who became an unrestricted free agent after he wasn't given a qualifying offer by the Chicago Blackhawks, had 48 points, including an NHL career-high 22 goals, in 69 games last season.
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Selected by the Arizona Coyotes with the No. 3 pick in the 2015 NHL Draft, Strome has 170 points (67 goals, 103 assists) in 273 regular-season games for the Coyotes and Blackhawks, and three points (two goals, one assist) in nine Stanley Cup Playoff games.
Strome's signing comes after a busy first day of free agency for the Capitals. They signed goalie Darcy Kuemper to a five-year, $26.25 million contract ($5.25 million AAV), goalie Charlie Lindgren to a three-year, $3.3 million contract ($1.1 million AAV), and defenseman Erik Gustafsson to a one-year, $800,000 contract on Wednesday. They also re-signed forward Marcus Johansson to a one-year, $1.1 million contract and acquired forward Connor Brown in a trade with the Ottawa Senators for a second-round pick in the 2024 NHL Draft.