Rasmussen has continued to be a crucial part of the Warriors starting line-up this season with 15 Guinness Premiership starts and four cup appearances.
Worcester Warriors Director of Rugby, John Brain, said: "Dale has established himself as a key player in our team over the last three seasons. He is a consistent performer who is hugely respected by both his opponents and peers. I'm delighted that he has chosen to make his major commitment to Worcester."
Speaking about his new deal, a delighted Rasmussen said: "I've thoroughly enjoyed my time at Sixways and I'm pleased to show my commitment to Warriors by pledging my future for another three years. I'm excited by the challenges ahead and the ambitious plans of this club. My family are also very settled in the area and I know they share my enthusiasm about the future."