The Scottish SPCA was alerted by a veterinary surgery who had been handed the dog by a concerned member of the public.
It had been found alone on Stillhouse Loan in Kirkliston and taken to a vets in Edinburgh.
Scottish SPCA inspector Stuart Murray said, “The dog is an elderly, female, black and tan crossbreed.
"We think she may be a Yorkshire terrier cross but unfortunately her condition was so poor it was hard to tell.
“She is microchipped but the chip is not registered so we have been unable to trace her owner so far.
“This poor dog was in an awful condition when she was found.
"She was covered in fleas, had overgrown claws and a skin condition.
“The dog was extremely matted and smelled terrible.
"She was so distressed she had to be sedated to be examined properly.
"During the examination it was discovered that the source of the smell was coming from matts that were so large they were starting to spread inside her mouth and cover her teeth.
“On veterinary advice it was decided that the kindest thing to do would be to put her to sleep and end her suffering.
“This is not the proper way to give up an animal if you can no longer care for them.”
Anyone has any information on this incident they can contact the Scottish SPCA’s confidential animal helpline on 03000 999 999.