It is believed around ten of the colourful birds have established themselves in and around the Royal Botanic Garden over the past few years.
Where the ring-necked parakeets originally came from is a mystery, though experts believe they are now perfectly happy living in the wild.
Ken Dundas, who lives in Fettes Village, said that one of the birds was a regular visitor to his garden and he had taken pictures of it on his bird feeder.
He said: "It is a lovely bird and it shares my bird nut cage with a lot of robins, chaffinches and blue tits. The estate is large, formerly part of the Fettes College grounds, so there's quite some space for the parakeet."
Gardener John Witherspoon, who tends properties in the area, said he had noticed the unusual bright green birds over the past few summers.
He added: "They've definitely been there for the last couple of seasons. At first I thought it was just one bird that was being let out by its owner but, after I spotted one a few times in the winter, I started to realise that they must be living in the wild.
"I've only ever seen one of them at a time, but they fly over the local playing fields and you always hear them in the trees along the main road.
"They are beautiful birds and you couldn't mistake them for anything else if you saw one or heard its screech.
"You wouldn't imagine that they would survive in the wild in Edinburgh, but they seem to be doing OK. They look like exotic pets so it's just amazing to think there's a population of them fending for themselves here."
A spokesman for the Royal Society for the Protection of Birds said that, although the species was originally from Africa and southern Asia, it was able to adapt to life in cooler climates.
He added that although the birds were popular as pets, there had been reports of escaped ring-necked parakeets starting breeding in south-eastern England – although they were rarely seen further north.
He said: "There's a very small population of naturalised parakeets in Edinburgh and the best place to see them is near the Botanic Gardens.
"They've basically escaped or been released and we believe that there are ten or so of them here now.
"They feed on seeds, peanuts and fruit and they have been around in the wild for a few years. We think that they are breeding, probably in hollow trees. The only danger to them is from predators. They're quite brighter than other bird species in this country. They could be at high risk of attack from sparrowhawks. Their climate is more tropical, but they have adapted well."