In return, the Caps got minor league prospect Tomas Fleischmann and two draft picks.
Going into weekend action, Lang was tied for the NHL scoring lead with 74 points. He appeared in 145 games for the Capitals the past two seasons.
"We have given Robert a chance to compete for the Stanley Cup while adding a good young player and two valuable draft choices to our organization," said Washington General Manager George McPhee.
Fleischmann, 19, is in his second season with Moose Jaw of the Western Hockey League.