The 21-year-old passed a medical on Monday and becomes new sporting director Oliver Kreutzer’s first recruit.
"He is still young, but has already a lot of experience in the Swiss league and he can continue to evolve," Kreutzer said.
Zoua scored 14 goals in 80 appearances during his four year spell in Switzerland, mostly as a squad player. He made his debut for his senior Cameroon national side last year.
"Hamburg is a great club and the Bundesliga is a big deal for me,” Zoua said after his move.
"Certainly the coach Thorsten Fink was also a reason why I decided for a transfer to Hamburg."
The signing comes after highly-rated South Korean attacker Son Heung-Min left the Imtech Arena to join Hamburg’s league rivals Bayer Leverkusen.
Leverkusen qualified for the 2013-14 Champions League with a third-placed finish, while Hamburg just missed out on Europa League football in seventh.