The striker's contract was due to expire in the summer of 2014, but he has now penned a fresh deal until 2017 with the Bundesliga club.
"I feel settled in Hanover and at this club. My next aim it to be a regular starter at the club," Sobiech told the club's official website.
"It's important for my development that I get more game time so I can also push for more international call-ups."
The 22-year-old came to the AWD-Arena in 2011 from Polonia Warsaw and while he has only scored six times in 37 league matches, he is clearly viewed as part of Hannover boss Mirko Slomka's future plans.
"Artur gives you everything you expect from a quality striker: goal-scoring instinct, assertiveness and athleticism," said sporting director Dirk Dufner.
"This early contract extension is a sign of our faith in him. I'm delighted that he will be a long-term part of the club."
Slomka added: "His potential and his attitude is outstanding. Artur has proved over the last two years, mostly as a substitute, that we can rely on him."