The thefts happened at about 6:15 a.m. Monday on Beaverdam Road Extension in Athens.
According to the reports, a man went onto the shelter's property and damaged the latches on three kennels, allowing three dogs to escape. One of the dogs was left behind at the shelter, but two of the dogs, a Chihuahua and Labrador, were stolen, the report said.
The perpetrator was described as a white man 20 to 27 years of age, about 6 feet tall, sporting a goatee and weighing between 170 and 190 pounds.
He was driving an older model Honda, the report said.