Two of the cubs are sisters who were found together on a flooded river bank in Earlston on Thursday.
The third cub was very weak and underweight when it was found in Brechin on Tuesday.
The Scottish SPCA said it was the charity's "busiest year" for otter cubs. It is currently caring for 14.
Colin Seddon, manager of the Scottish SPCA's national wildlife rescue centre in Fishcross, said: "The cubs found on the river bank in Earlston had a very lucky escape as it was a difficult rescue for our officer in the dark.
"Despite their ordeal, the cubs are doing well. They are sisters who are around 10 weeks old and are self-feeding. They don't need much attention from our staff as they have each other."
He said the otter found in Brechin was about 12 weeks old.
Mr Seddon added: "His body weight is only 50% of what it should be but he is feeding himself and we are hopeful he will make a full recovery. He will soon be put in with the girls to make a group of three.
"Typically, otter cubs will remain in the care of our wildlife centre for around a year, as this is how long they would stay with their mother in the wild.
"We are hopeful the otters will be returned to their natural habitat after this point."
Three orphaned otter cubs are being cared for by a Scottish animal charity after they were found alone without any sign of their mothers.