The Wizards will send forward Jan Vesely to the Nuggets and point guard Eric Maynor to the 76ers, who also will get two second-round draft picks.
Miller hasn't played since he was suspended by the Nuggets on Jan. 2 after an altercation with coach Brian Shaw.
Miller is earning $5 million this season, and his $4.6 million contract for next year is guaranteed for just $2 million. The 16-year veteran averaged 5.9 points and 3.3 assists in 30 games for the Nuggets.
Washington (26-28) is fifth in the Eastern Conference, 2 1/2 games out of the fourth spot.
Vesely, the No. 6 pick in the 2011 draft, has averaged just three points and three rebounds in 33 games for the Wizards.
Maynor, who was signed as a free agent in the offseason by the Wizards, has fallen out of the rotation and averaging 2.3 points per game. He has a player option for $2.1 million next season that the 76ers will assume in exchange for the draft picks.