The team announced the contract Friday during NHL All-Star Weekend, which is taking place in south Florida -- where the draft was held in 2015 when Strome was picked third overall.
Strome will count $5 million against the salary cap through the 2027-28 season. He was set to be a restricted free agent this summer.
"Dylan is an intelligent and skilled center and has been a great addition to our organization," general manager Brian MacLellan said. "We are pleased to sign him to a long-term contract. We feel his skill set is a great fit for our team as he enters the prime years of his career at an important position."
Strome is getting a raise from the $3.5 million deal he signed with the Capitals after the Chicago Blackhawks opted not to tender him a qualifying offer and made him a free agent. Strome has 11 goals and 25 assists in 36 games this season and ranks third on Washington's roster with 14 power-play points.
The Mississauga, Ontario, native who played his junior hockey alongside Connor McDavid with the Erie Otters has 206 points in 325 regular-season NHL games with the Arizona Coyotes, Blackhawks and Capitals.