Brunt turned down a new deal in the summer after The Owls rejected a bid from Fulham during the pre-season break.
The former Middlesbrough man has a burning desire to play in the Premiership and he feels he will have a better opportunity to do so at West Brom instead of Hillsborough.
The Owls have accepted an undisclosed bid which matches their value of the player - a fee around the £3million mark.
Brunt played in the 4-1 defeat at Ipswich on Saturday but will miss the next three games, for whichever team he is contracted to, after a sending off in Holland.
Wednesday have confirmed that Brian Laws will be able to use some of the money on new players and the club are currently talking to a number of potential new midfielders to replace Brunt.