He revealed his illness in an interview with host Mary Hart of "Entertainment Tonight." The segment was to air Monday night on the entertainment news magazine.
"I feel great, the prognosis is excellent," Cojocaru told Hart. He's been assured by his doctor that after the operation, "I can climb a mountain in Nepal."
Cojocaru, being treated by Dr. Stanley Jordan of Cedars-Sinai Medical Center, was diagnosed with the disease during a general checkup.
"The healthy thing for Steven to do is to continue working," Jordan said. "Steven will live a normal life after the transplant. He is coming to us in a very good state because he has been on a very healthy diet already."
A donor has yet to be found for Cojocaru, a Paramount spokeswoman said Monday.
Cojocaru, who became known for his denim-and-fur wardrobe and snappy assessment of celebrity awards-show fashion, said he is continuing to develop a talk show for next fall.
Polycystic kidney disease is a common hereditary disease that affects about 600,000 Americans, according to Cojocaru. It often goes undiagnosed until a person reaches their 30s or 40s, he said.
Cojocaru, a contributor to NBC's "Today" show, is around 40. His exact age was unavailable, according to Paramount Domestic Television, which distributes "Entertainment Tonight" and "The Insider."
The disease causes cysts to grow in both kidneys, diminishing functioning tissue, according to the "Merck Manual of Medical Information." When symptoms occur, they can include back pain and blood in the urine.
More than half of those with the disease, which can become evident in childhood or in later life, develop kidney failure at some point and require dialysis or kidney transplantation, the "Merck Manual" said.
Kidney transplant surgery is second to corneal transplant as the most common transplant operation in the United States, with over 9,000 kidney transplants performed each year, according to Paramount.