The 21-year old has spent the last four years with the Swiss club, winning the league title four times since joining as an 18-year old.
Zoua was a reported target for the Baggies, but he spoke of his delight upon his move to Germany.
"Hamburg have shown more interest in me than any other team in the world so that is why I am here signing a contract," he told skysports.com.
"There was an English team interested but it cooled at the last minute.
"I am happy to be at Hamburg and hope to make the fans happy by scoring goals for them in the Bundesliga which has become the top league in the world for me."
Meanwhile, Borussia Dortmund's German under-21 international Lasse Sobiech says that he is hoping to make the switch to Hamburg with chances of first-team action at the Westfalenstadion limited.
"It is a fact I have been in touch with Hamburger SV. We have had a lot of talks and negotiations and I am very keen on this," he said.
"I am hopeful to see a final decision taken on this very soon."