The fee is in excess of £13million and significantly higher than the initial £10million the club paid Tottenham for Darren Bent last summer.
Bruce will hope for a similar return from Gyan, who has signed a four-year contract at the Stadium of Light.
He said: "As anyone who has watched Ghana recently or who watched the World Cup will tell you, Asamoah is a real livewire.
"He had a fantastic tournament in the summer and a lot of European clubs sat up and took notice.
"I have been very keen to bring in another striker to add to the quality we have, but only when we felt the deal was right.
"We feel this is a great deal for the football club and Asamoah really wants to be here and in the Barclays Premier League, so I'm delighted he has joined us."