The Wizards didn't announce terms of the deal. Published reports last week said the two sides agreed on a five-year, $35 million contract.
Brooks, 50, didn't coach last season after being fired by Oklahoma City. He went 338-207 with the Thunder and reached the NBA Finals in 2012.
"I am beyond thrilled to return to coaching with a team that is filled with such potential and to be able to join an organization that is committed to helping us reach our goals," Brooks said in a statement. "I'm very grateful to (owner) Ted Leonsis and (president) Ernie Grunfeld for this opportunity and I can promise the great fans of Washington that we will work extremely hard both on and off the court to represent them in a manner fitting the most powerful city in the world."
Washington went 41-41 this season and missed the playoffs. The Wizards are hoping Brooks will turn into a perennial playoff participant.
"Scott was our top candidate and we moved quickly on an agreement to make him our head coach," Grunfeld said in a statement. "His presence, the core players we have returning and our cap flexibility this summer have us all looking forward to the possibilities of what our team can accomplish."
One possible target is Oklahoma City forward Kevin Durant, who will be a free agent this summer.
The Washington D.C. native had a solid relationship while spending eight seasons in Oklahoma City with Brooks -- the last seven with Brooks serving as head coach before being fired after the 2014-15 campaign.
Brooks had four 50-win campaigns with Oklahoma City -- including 60 in 2012-13 -- and reached the Western Conference finals on three occasions.
"Scott's approach to the game, track record for player development and ability to communicate with his players made him the clear-cut choice to guide our team as we continue to rise as contenders in the Eastern Conference," Leonsis said in a statement. "His accomplishments as a coach are matched only by his sterling reputation around the league and we're confident that our fans and players alike will embrace and support him as he leads the way."
Before his coaching career, Brooks played 10 NBA seasons with six clubs and averaged 4.9 points. He played college basketball at UC Irvine.