Young, 27, a four-time All-Star, joins Washington near the mid-point of his eighth season with Atlanta.
ESPN said Young had been keen to join the Wizards, where he will be reunited with Washington executive Travis Schlenk, who drafted him in 2018.
Washington, who are one place off the bottom of the Eastern Conference with a 10-26 record, view Young as the centerpiece of their rebuilding project.
Young, who has averaged just over 25 points a game through his career, has struggled for form and fitness this season, playing in just 10 games for Atlanta after suffering knee and thigh injuries.
He has not played since suffering a right quadriceps contusion on December 27.