The Sharks have also agreed to retain 50 per cent of Dillon’s salary and cap hit in the exchange.
“Brenden is an experienced defenceman who plays a solid defensive game with a high compete level and physicality,” said Capitals general manager Brian MacLellan in a press release.
“We felt it was important for us to add a player of his caliber to our defensive group.”
The 29-year-old has recorded 14 points in 59 games with the Sharks this season.
The native of New Westminster, B.C., has 88 points across 439 games with the Sharks.
The six-foot-four, 225-pound defenceman began his career with the Dallas Stars.