The 25-year-old has signed a three-year contract at the Hawthorns and will wear the No.9 shirt after agreeing personal terms and completing a medical.
Head coach Alan Irvine says the striker will bring great experience to the West Brom attack as he becomes the club's fifth signing of the summer.
“Brown is a quality striker and I’m looking forward to working with him," he told the club's official website.
“He’s a strong, quick, powerful player who likes to get in behind defences and has plenty of Champions League and international experience.”
Ideye joins the club from Dynamo Kiev, where he spent three seasons, scoring 34 goals in 74 appearances and technical director Terry Burton is backing him to bring goals to the Hawthorns
“It is a fantastic signing because of the quality and the potential of the player," he added.
“I can see that he really wants to be here and that he really wants to be playing in the Premier League.
“He’s a dynamic player who likes to get in behind defenders and he has the pace to do so.
“He gets himself into good scoring positions in the box and if there are opportunities then he will get on the end of them.
“We’re looking forward to seeing him play for the club and scoring goals.”