The defenseman has 14 points (one goal, 13 assists) and 83 penalty minutes in 59 games for the Sharks this season. He is in the final season of a five-year contract and can become an unrestricted free agent July 1.
"I'm really excited. I can't wait to get there," Dillon said Tuesday about Washington. "The team, the group, what an opportunity.
"I've tried to bring the lunch pail to work every day and do my job, but definitely I'm going to be happier to get going."
Signed by the Dallas Stars as an undrafted free agent on March 1, 2011, Dillon has 114 points (22 goals, 92 assists) in 588 NHL games with the Stars and Sharks, and nine assists in 62 Stanley Cup Playoff games.
He said the constant trade talk has taken a toll on him and his Sharks teammates.
"It's been crazy. It really has," Dillon said. "I think as you start to lose, the Canadian swing where you're going through a little more media, it ends up being where more of the questions get raised, what's going to go on, especially being a pending UFA. If you're a team that's not really in the race -- we won four of our last five here with the Sharks and we're still almost in the same position in the standings -- it's just too tough to get back into the race. I think mentally guys can say they don't read this or they don't read that, but it wears on you, for sure."
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Washington general manager Brian MacLellan said he anticipates Dillon being a good fit in the Capitals back end.
"He's got playoff experience, he's a veteran player, physicality, the ability to play with top-end guys, a good character guy," MacLellan said Wednesday. "I think he'll add a lot of energy in our room and on the ice. He's a physical presence. He checked a lot of boxes for everything we thought we needed.
"I think we move him around a little bit. He could play with [ John Carlson ], could play with [ Dmitry Orlov ]. He's played with two good guys in San Jose. I anticipate the coaches trying him at both spots and see what works best for us."
The Capitals (37-17-5) lead the Metropolitan Division, one point ahead of the Pittsburgh Penguins, but are 3-6-0 in their past nine games. MacLellan said Washington still would have pursued a trade for Dillon even if it hadn't been struggling of late.
"Probably regardless, because I think it's a great fit for us," he said. "I think one of the things that's been frustrating for me is the play in front of our own net, the compete level in front of our own net, and this is something he brings to the table here. I think he does a great job in front of our net. So I think we addressed that through him."
The Sharks (26-29-4) are 12 points behind the Coyotes for the second wild card into the playoffs from the Western Conference.
Washington and San Jose are off until Thursday, when the Capitals host the Montreal Canadiens at Capital One Arena (7 p.m. ET; NBCSN, NBCSWA, TSN2, RDS, NHL.TV), and the Sharks begin a four-game road trip against the New Jersey Devils at Prudential Center (7 p.m. ET; MSG+, NBCSCA, NHL.TV).
NHL.com staff writer Tom Gulitti contributed to this report
