Owner Diane Cowie, 52, said she almost fainted when Lola began scratching at the kitchen door of her Colinton home, having been missing since January.
The Evening News previously told how police were investigating witness reports that two children – thought to be aged around eight and 13 – were seen walking off with a cat in their arms around the time Lola vanished.
She had been in the family’s front garden in The Gallolee while Diane and her husband were out shopping and had vanished before they had returned.
Mrs Cowie said: “I was in the kitchen making breakfast on Sunday morning and heard a scratch and a miaow and thought it was the cat from the next door neighbour’s house. But when I saw it was Lola I just about collapsed, but just wanted to get her indoors.
“My daughter, who found Lola as a stray, is up for the weekend and thought I was playing an April Fool’s joke but was delighted when she found out it was real.”
Mrs Cowie said she has no idea where the fugitive feline could have got to – but still suspects foul play.
“We don’t know what happened to her or whether she’s been living rough for a few days before she got back,” she said.
“We could go on second-guessing forever how she’s managed to get home.
“I still think she was probably taken and has lived as a house cat for the last few months.
“But judging by the size of her she’s not been mistreated because she’s put on a tonne of weight.
“We were keeping in touch with the rescue centre, who said that cats will come back in their own time and especially in fine weather. You will not keep a cat indoors who is determined to get out.”
Mrs Cowie was able to identify Lola by a distinctive “tea stain” under her chin, while a vet confirmed the news by checking her microchip.
Lola, who returned with a small cut to her nose, is said to be spending time in the conservatory basking in the recent sunshine as she adjusts to life back home.
Ms Cowie said: “The whole thing was quite a shock. It’s just disbelief that she’s home and, it might sound dramatic, but we just cried with joy.”
Lola has been prescribed a strict low-fat diet as she slims down to her pre-adventure weight.
A police spokesman said: “We were pleased to hear about Lola’s safe return.”