The 30-year-old forward, in the final season of a four-year contract he signed as a member of the Anaheim Ducks on Aug. 14, 2015, can become an unrestricted free agent July 1. He has eight points (two goals, six assists) in 38 games this season with the Kings and Pittsburgh Penguins, who traded him to Los Angeles for forward Tanner Pearson on Nov. 14.
Hagelin was acquired by the Penguins in a trade with the Ducks on Jan. 16, 2016. He won the Stanley Cup with Pittsburgh in 2016 and 2017.
RELATED: [2018-19 NHL Trade Tracker]
"[Hagelin is] a player we are really excited about having join our team," Capitals coach Todd Reirden said. "... A huge, huge gain for us in terms of speed, experience and the championship experience as well. We see him being a big part of our penalty kill and continuing to try to make that better.
"We saw him the last couple of weeks and we've been watching him for a while. ... We also feel the style of play we have is different than the style he's been playing in Los Angeles systematically, so we feel this will allow him to use his speed a little bit more and be a factor that way."
Selected by the New York Rangers in the sixth round (No. 168) of the 2007 NHL Draft, Hagelin has 230 points (90 goals, 140 assists) in 526 regular-season games and 47 points (22 goals, 25 assists) in 121 Stanley Cup Playoff games.
Hagelin will not play when the Capitals visit the Toronto Maple Leafs at Scotiabank Arena on Thursday (7 p.m. ET; ESPN+, TVAS, TSN4, NBCSWA, NHL.TV), but is expected to make his Washington debut at the Buffalo Sabres on Saturday.
The Kings visit the Nashville Predators at Bridgestone Arena on Thursday (8 p.m. ET; NBCSN).
NHL.com correspondent Dave McCarthy contributed to this report