Police Lt. Mark Ketterer said that it happened last week in the riverfront Tremont neighborhood overlooking downtown Cleveland.
A CSX bridge monitor found the survivor Friday night and called police.
The worker told police that he witnessed from a distance the dog being tied to the tracks and someone appearing to take photographs or video of it.
By the time the railroad worker got to the dog, the train had passed and the man was gone. The bodies of the other dogs were found in the same secluded stretch of tracks.
After a mandated waiting period to allow the owner to reclaim the dog, the survivor will be offered for adoption after Friday, Cuyahoga County animal shelter manager Lesley DeSouza said Wednesday.
The shelter has been getting three email or phone inquiries an hour about adopting the dog, a mixed breed about 22 pounds and 14 inches tall, she said.
"She's very gentle. She's playful. She's about 2 years old," DeSouza said. "She is amazingly friendly, and she likes to sit on your lap. She's a lap dog. We're just stunned that a dog that went through all this so quickly has adapted herself."
The survivor had a pink collar that might indicate that she was someone's pet, DeSouza said.
"We don't know if these three dogs were related, if they came from the same family," she said.
The remote location without nearby homes suggests the man wanted to harm the dogs without being noticed, DeSouza said.
"Somebody purposely took dogs down to the railroad tracks. It's an isolated area. The chances of being observed are very slim. Obviously, somebody did see him," DeSouza said.