The former Dynamo Kiev man becomes the fifth summer signing of the Baggies and has beat Stephane Sessegnon's 5.5 million pounds record transfer from Sunderland last year.
Ideye, 25, was part of the Nigeria squad that won the Africa Cup of Nations title in South Africa last year. He scored a goal in the semi final 4-1 routing of Mali.
However, he was dropped from the provisional World Cup squad by coach Stephen Keshi in May.
According to West Brom, the striker who will wear number 9 has signed a three year contract with the option of an additional year. He has since passed a medical at the Hawthorns and agreed to personal terms.
Ideye has had stints with Ocean Boys, Neuchatel Xamax, Sochaux and Dynamo Kiev and has played in the Uefa Champions League.
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.”
Technical director Terry Burton added: “When I arrived at Albion the recruitment department flagged Brown up as the man at the top of their wish list.
“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 then he will get on the end of them.
“We’re looking forward to seeing him play for the club and scoring goals.”
Even though the exact amount was undisclosed, the Nigerian has become the club's record signing, beating Stephane Sesegnon's 5.5 million pounds transfer from Sunderland last year.