The Slovak goaltender has been traded for the second time in six days, as the Sabres sent him to Washington just before the NHL trade deadline.
Halak was dealt to the Sabres by St. Louis last week in a move that saw the Blues acquire star goaltender Ryan Miller.
He was on the bench for one game with the Sabres, backing up Jhonas Enroth.
Halak posted a record of 24-9-4 with a 2.23 goals-against average and a .917 save percentage in 40 games with the Blues this season.
He has some history with the Capitals, beating them in the first round of the 2010 playoffs while with the Montreal Canadiens after Washington won the Presidents' Trophy.
Through eight NHL seasons in Montreal and St. Louis, Halak a 139-81-26 record with a 2.38 goals-against average and a .917 save percentage in 260 appearances.
Neuvirth has posted a 4-6-2 record with a 2.85 goals-against average and a .914 save percentage in 13 games with Washington this season.
Klesla collected four points (one goal, three assists) and 24 penalty minutes with the Phoenix Coyotes this season.
He didn't get into a single game with Washington after being acquired Tuesday in the trade that sent Martin Erat to the Coyotes.