The 25-year-old has signed a three-year contract, with an option for a further 12 months, after agreeing personal terms and passing a medical.
Ideye has been handed the No.9 shirt and moves to The Hawthorns for an undisclosed fee, widely reported to be £9m.
“Done deal, officially a West Bromwich Albion player, thank you god,” Ideye tweeted. “Dream come true ... EPL. Would like to thank my family and my agents."
The former Sochaux and Neuchatel Xamax forward has netted 33 goals in 74 matches for Dyanmo Kiev and scored five times in 23 appearances for his country, but was overlooked for this summer’s World Cup in Brazil.
“Brown is a quality striker and I’m looking forward to working with him,” manager Alan Irvine told Albion’s website.
“He’s a strong, quick, powerful player who likes to get in behind defences and has plenty of Champions League and international experience.”
Technical director Terry Burton added: “It is a fantastic signing because of the quality and the potential of the player.
“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 the he will get on the end of them.
“We’re looking forward to seeing him play for the club and scoring goals.”
The player’s representatives, Hootan Ahmadi and Ali Barat, confirmed the player rejected several other offers to make the move to West Brom.
They said: "A number of clubs expressed an interest in Ideye, but West Brom worked hard to get him. It is a club record deal and it shows how highly West Brom value him.
"Ideye has always wanted to play in the Premier League and he is really looking forward to the start of the season. He has scored goals where ever he has been I'm sure he will do the same and show his quality at West Brom.”
Albion previously broke their transfer fee record when they splashed out £6m on Stephane Sessegnon last September.