The two clubs agreed terms over a fee on Friday night.
Bruce said: "When he burst onto the scene at Rangers I saw him play with (Sone) Aluko and I liked what I saw.
"He had a wonderful time in Scotland, came down here and had a wonderful year with Everton. This year he has found it frustrating but we watched him again against QPR and he reminded us all what a good player he is. We'll try our best.
"He's big, strong and powerful, and he's got a goalscoring record that's there for everyone to see."
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