Ideye, 25, signed a three-year contract, with an option for a fourth, with the Premier League club after agreeing to leave the Ukrainian outfit.
He moves to the Hawthorns for an undisclosed fee in excess of that paid for Stephane Sessegnon when the midfielder moved from Sunderland last year.
“Albion have signed Nigeria international striker Brown Ideye from Dynamo Kiev for a club-record transfer fee,” a statement on the club’s website announced.
Albion head coach Alan Irvine believes Ideye has all the attributes needed to succeed in the Premier League.
“Brown is a quality striker and I’m looking forward to working with him,” he said.
“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 been handed the Albion number nine shirt and will join up with the squad when they return from a pre-season training camp in California.
He scored 34 goals in three seasons with Dynamo, having previously played for Sochaux and Neuchatel Xamax after starting his career in his homeland with Ocean Boys.
He has won 24 caps for Nigeria, scoring five times including in the semi-final as the Super Eagles won last year’s African Nations Cup.