The attacks in San Bernardino County began shortly after 8 a.m. Wednesday morning, authorities said.
Deputies reported to the scene where the dogs had just killed a goat and were attacking other goats in the pen, the Los Angeles Times said.
Animal control officers attempted to capture the dogs but one of the pit bulls then began charging a deputy.
The deputy shot and killed the pit bull.
A second pit bull then tried to attack the deputies, and one of the officers opened fire, killing the dog, the Times said.
Deputies were able to capture the third dog.
Witnesses told investigators there have been previous incidents with the dogs, which did not have collars or identification tags, the Times said.
Deputies went to a home where the owner was reportedly living, but no one was there.
Authorities said the investigation is ongoing.