Leicester City will complete the deal for £2million striker Chris Wood when the transfer window opens on New Year's Day.
The 21-year-old New Zealand international will then move from West Brom to the King Power Stadium.
Wood has agreed a three-and-a-half year contract with City and the deal is reportedly worth £1.25m, potentially rising to £2m.
Officials at City confirmed the deal in a short statement last night.
The statement said: "Leicester City can confirm that an agreement has been reached with West Bromwich Albion for the transfer of Chris Wood.
"He has agreed personal terms with the Foxes, with a view to completing a permanent transfer once the January transfer window opens."
However, their counterparts at West Brom were more forthcoming at their weekly press conference yesterday.
Albion coach Keith Downing, speaking before today's trip to face Manchester United at Old Trafford, said Wood was "focused" on his move to City.
Downing said talks were advanced and Wood had been recalled from his loan spell at Millwall, but would not be considered for the Albion squad this weekend, as the deal was set to be completed.
"The Leicester thing is advanced and the situation there is that he's focused on the move," he said.
"The January window isn't open but we've brought him back. I've worked with Chris for a number of years. He has done exceptionally well at Millwall and Leicester have shown an interest.
Wood has scored 11 goals in 19 appearances on loan at Millwall this season. The Lions were keen to make his stay at The New Den permanent, and have been angered by the player's decision to go to City.
Millwall director Peter Garston said the Lions had matched City "in every financial aspect" of the deal.
"I know the salary, transfer fee and all the add-ons that were offered to both West Brom and the player, and I can assure everyone we matched Leicester in every financial aspect.
"Be assured, the board went to extreme lengths to get him at the club permanently. As with all transfers, the final decision is with the player as to whether he sees his future at a club.
"As I understand it, Wood and his agent felt there was more chance of him getting Premier League football with Leicester. Personally, I find this very annoying as it was only two weeks ago that Chris echoed thoughts of staying with us."
