Bruce shelled out a club-record £13m to sign the 24-year-old on the final day of the summer transfer window.
"I've absolutely been impressed with his character," Bruce told safc.com.
"He missed a big penalty against Uruguay but dusted himself down and stuck the second one in the top corner in the shoot-out.
"Everyone remembers that miss from Asamoah; Ghana were minutes away. Let's be fair, it was an injustice with the handball off the line, then he missed the penalty.
"I've been chasing him for about three or four years but never been able to afford him. Thankfully, we got it done this time."
And Bruce believes he's signed a player who can add "something different" to the Sunderland attack, adding:
"Asamoah's a typical number nine. He led the line himself for Ghana and for Rennes in France. He is used to playing alone and wants to lead the line.
"To get the best out of Benty, Danny [Welbeck] and Fraizer Campbell too I think we need a player like him."