Keith and Sue Webb received the unmarked portrait at their home in Winchester, Hampshire on Wednesday.
It had no covering letter and Mrs Webb banished it to the garage, calling the woman pictured a "horrid old crone".
A relative in Australia has told Mr Webb she recognised it from his late uncle's house, where it once hung.
Mr Webb, an 82-year-old industrial property landlord, now hopes to keep the portrait in the family, having initially shown a dislike to it.
But he still does not know who sent the painting in the post.
"I believe it's a portrait of my great, great grandmother," Mr Webb said.
"Alison, my late cousin's wife in Perth, Western Australia saw the initial story about Sue and I being sent the picture and solved the mystery.
"She remembered staying with my uncle, Charles Webb, in Winchester in the 1970s and that the painting used to hang on his bedroom wall.
"Her daughters were absolutely terrified of it and wouldn't go near it."
Mr Webb was his uncle's executor when he died, but understands the picture was given to his younger brother Leigh.
"Having initially been so rude about the painting, it now turns out it's come from within the family," he added.
"There's been interest from one of my children who might like to hang it in a holiday home he lets.
"But in the meantime, Sue's insisting it's not moving from the garage."
Mr and Mrs Webb took the portrait to a local auctioneers who told them it was between 200 and 300 years old and worth about Â£200.
A couple have solved the mystery of who owned an oil painting depicting an "ugly" woman which was posted to them without explanation.