Davis said he got the news from surgeon Dr. Bob Evani, who removed the pitcher's cancerous thyroid gland on April 10.
"The cancer did not spread and it will not spread from here on out," Davis said Thursday.
He underwent a "nuclear CT scan," which would detect any spread of the disease.
"I shook Dr. Evani's hand, told him what a great job he did and what a great doctor he is and just was grateful," Davis said. "I hugged my fiancee and we got out of there, because nobody likes to stay in the doctor's office more than they have to."
The cancer was discovered before the season began but Davis had two starts before undergoing the surgery. He allowed two runs in six innings in a 10-5 victory over the Los Angeles Dodgers two days before the surgery.
Davis is scheduled for two rehab starts for Triple-A Tucson, on Saturday and next Thursday. He is to have another CT scan in six months.