Polanski, 26, has signed a contract until 2015, the club's third acquisition in four days after the arrival of defender David Abraham and Ghana international defensive midfielder Afriyie Acquah earlier this week.
"We have at Hoffenheim a very tough task ahead of us and we are fully aware of that," said Polanski. "I am convinced we can stay up and am just happy to be here and help out."
Hoffenheim occupy the relegation playoff spot with 13 points from 18 matches, one more than Augsburg. Greuther Fuerth are bottom with nine points.