Ideye, who cost the Baggies a reported £10million from Dynamo Kiev, joins Victor Anichebe, Saido Berahino and youngster Adil Nabil in Irvine’s pool of attacking options, but the new manager would like to add more.
Albion have made six new additions to their squad this summer – including Ideye – with Craig Gardner, Joleon Lescott, Chris Baird, Sebastien Pocognoli and Andre Wisdom all completing moves to the Hawthorns.
Costa Rica full-back Cristian Gamboa is also understood to be on the verge of joining and Irvine says that their transfer activity will not stop there, with an additional striker his priority.
"We’ve got Brown in now so that gives us three recognised strikers at the right level, and it would be lovely to have another one, but of course strikers cost a lot of money," he told the Birmingham Mail.
"We have a budget to work to and rightly so, and it’s a case of trying to stretch that as well as we possibly can.
"I would love us to be able to get in another striker because you want to have options of how you can play up front, but having said that I’ve been absolutely delighted with Victor Anichebe and Saido Berahino, I think they’ve been terrific since I came in, day in and day out in training.
"Nothing happens in a hurry now - unfortunately deals take a long long time.
"Many things that you work on behind the scenes don’t actually come to fruition, so people only really see what you manage to complete.
"That doesn’t actually reflect the hard work that’s going on back at the club by many people, from the chairman right the way through, there’s a lot of hard work being done, but not everything comes off."