No terms were disclosed, but media outlets reported that his contract is worth $18 million over four years.
A news conference is scheduled Thursday to introduce Saunders.
Saunders, 54, compiled a 587-396 record in 13 seasons with the Minnesota Timberwolves and Detroit Pistons.
He inherits a team that went 19-63 this season, the worst record in the Eastern Conference.
"He has great sets," guard Gilbert Arenas told The Washington Post. "He's a very great X's and O's guy coming out of timeouts. If we're using the offensive plays they were running, then I should be atop the assists."
Most of the record was under the guidance of interim head coach Ed Tapscott, who took over when Eddie Jordan was fired after Washington lost 10 of its first 11 games.
"We need somebody to really be like, 'Don't try to just outscore teams," forward Antawn Jamison told the newspaper.