The Capitals announced the move Monday, less than a week after Boudreau reached 200 wins faster than any coach in modern NHL history.
But the Capitals have otherwise been struggling, losing six of their last eight to fall to eighth place in the Eastern Conference despite a talented lineup led by two-time league MVP Alex Ovechkin.
Boudreau was hired four years ago on Thanksgiving Day. He went 201-88-40 in the regular season with the Capitals but just 17-20 in the playoffs.
The 51-year-old Hunter played 19 seasons in the NHL and is one of four players to have his number retired by the Capitals.
He makes his debut Tuesday against the St. Louis Blues.