Sources told KickOffNigeria.com however that the total could rise to as high as £13.5 million.
Ideye, who won the African Nations Cup with Nigeria but was inexplicably left out of the World Cup squad, joins from Ukrainian club Dinamo Kyiv.
The forward was at West Brom on Friday morning to sign the deal, and has been handed the number 9 jersey.
Ideye says he is thrilled by the move.
"The English Premier League is the best in the world and I look forward to having a successful time here," he told KickOffNigeria.com.
Ideye started his career at Nigerian club Ocean Boys, but moved to Swiss side Neuchatel Xamax then moved to Sochaux before joining Kyiv in 2011.
He was called in as a last minute replacement for the injured John Mikel Obi for the 2010 World Cup, and played a pivotal role as Nigeria won the African Nations Cup in 2013.
He also represented the country at the FIFA Confederation Cup in 2013 before being surprisingly cut from the 2014 World Cup squad.
Ideye will become the fifth Nigerian to play for the Baggies, following in the footsteps of Ifeanyi Udeze, Nwankwo Kanu and more recently Osaze Odemwingie and Victor Anichebe and he says he looks forward to carrying on the proud Nigerian traditions at the club.
