The 17-year-old became Hamburg's youngest ever Bundesliga player when he made his debut against Hertha Berlin in August, and has made nine appearances so far this term.
After a slow start to the season, which cost Thorsten Fink his job as coach, Hamburg have climbed into mid-table in the Bundesliga under the guidance of new boss Bert van Marwijk, and Tah has been an important part of that revival.
Tah, a Germany Under-17 international had only signed his first professional deal in the close-season, but the Lower Saxony outfit have moved quickly to tie him down and ward off attention from other clubs.
"I am delighted with the trust (shown in me)," Tah told the club's official website. "For me it was always clear that I wanted to continue playing here.
"I am still at the very beginning (of my career) and would like to improve every day. I am pleased that the club gives me the chance to do so."
Sporting director Oliver Kreuzer was delighted to secure Tah's future and predicted a long and prosperous career for the teenager.
"We are glad that we were able to tie a homegrown player to the club," he said.
"We have taken his development very positively and now want to lay the foundations for a long-term collaboration."
