He has penned a three-year deal with a further year’s option if the Baggies still want him.
Head coach Alan Irvine said: “Brown is a quality striker and I’m looking forward to working with him.
“He’s a strong, quick, powerful player who likes to get in behind defences and has plenty of Champions League and international experience.”
Ideye has scored 33 goals in 74 for matches for the Ukrainian side and other former sides include Sochaux in France and Neuchatel Xamax in Switzerland.
Capped 23 times by the Super Eagles with five goals, he was part of Nigeria’s African Nations-winning squad last year but did not travel to Brazil for the World Cup.
The fee will eclipse the £6m spent on Stephane Sessegnon last year in what is a statement of intent from the Midlands club after their narrow escape from relegation.
Ideye will link up with his new team mates when they return from their pre-season training camp in the United States.
Meanwhile, the Baggies have also agreed a fee with Derby for wantaway midfielder George Thorne believed to be in the region of £2m.
The Baggies had already knocked back two bids for the 21-year-old.
The midfielder starred for the Rams while on loan last season and recently had a transfer request turned down by Albion.
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