The popular visitor attraction, which welcomes about 200,000 people a year, is home to a variety of animals including sheep, pigs, ducks, geese, chickens and a number of smaller animals. The animals at the farm will be looked after until new homes are found for them.
A total of 18 jobs will be lost as a result of the decision.
The Evening News spearheaded a £100,000 appeal campaign to keep the much-loved attraction open three years ago when it faced soaring running costs and a slump in external funding.
The farm has attracted visitors for more than 40 years but financial struggles in recent times has led to the closure of the site’s cafe.
Following today's announcement, Gorgie City Farm chairman George Elles said: “Falling revenues due to a decline in external funding, and rising costs, have made it impossible for Gorgie City Farm to continue to provide our services to the community in Edinburgh.
“We were buoyed by the successful appeal three years ago but sadly cannot find a route to a sustainable future in the current funding climate.
"We are sincerely grateful to all our staff who have worked tirelessly to provide much needed services and an accessible amenity for the city, and to our volunteers who have been inspired by the opportunities and support we have been able to offer. We don’t underestimate what this decision will mean to them all and are full of pride of what they have achieved.”
Gorgie City Farm has welcomed around 200,000 visitors a year since it was saved from closure in 2016 after a successful crowdfunding appeal raised in excess of £100,000.
As well as being a visitor attraction, it is also a working farm and provides assisted volunteering experience for hundreds of people each year who face barriers to employment.
It receives funding from Edinburgh City Council, various grant giving trusts and individual donors and generates additional income through its cafe and animal boarding service.
Shona Campbell of MHA Henderson Loggie has now been appointed to wind up the 40-year-old charity, which operates from a site to the west of the city centre.
Ms Campbell said: "The trustees have reached the responsible decision wind up the charity with regret after exploring all options open to them in the face of a tough funding climate.
“It is always difficult when people lose their jobs through no fault of their own and we will now undertake to act as efficiently and sensitively as possible to provide support in matters concerning staff and volunteers.
"The welfare of the animals being cared for at Gorgie City Farm is equally important and they will be well looked after until new homes are found for them."