The deal was formally agreed on Wednesday when Kilbane passed a medical at The Stadium of Light.
He had agreed the terms of the deal, reportedly worth £2.5 million, on Tuesday night and thus missed his side`s draw with Grimsby
Kilbane had attracted interest from Liverpool and West Ham, before he eventually decided to join Sunderland.
In a statement, Wile explained that the club did not want a repeat of the Andy Hunt situation, where a top player was lost under the Bosman Ruling.
The statement read: "West Bromwich Albion FC have today accepted an offer from Sunderland FC for the transfer of Kevin Kilbane.
The player and his agent informed the club that they would not be prepared to re-negotiate a new contract to replace the current agreement which expires at the end of next season.
In view of the implications of the Bosman Ruling, Kevin would have been able to leave the club for nothing in the summer of 2001.
Further to the loss of Andy Hunt in similar circumstances, the decision to transfer Kevin at this time has been taken in the best interests of West Bromwich Albion FC."
Jonny Wootton
