"We're obviously delighted Kanu has decided to join us," Baggies boss Gary Megson told the clubs official website.
"I felt it was important we signed this type of player as I think it takes us forward not just one step but quite a few steps.
"One of the things I mentioned to Kanu was that we would be bringing in other players. And while he will make a difference to us, it's important we don't just think this signing will transform us overnight, although it is a massive signing for us."