HMS Edinburgh has been put on sale after Edinburgh City Council decided that preserving it as a tourist attraction would be too expensive.
Following calls from the council's Lord Provost, a report was commissioned to establish whether it was economically viable to preserve the ship.
The report found that the costs were too high.
The ship is on sale, along with HMS York and HMS Gloucester, on the Ministry of Defence (MoD) website.
The Disposal Services Authority (DSA), which the MoD used to dispose of surplus material, originally listed the ship for sale in August 2012.
Edinburgh City Council asked Pricewaterhouse Coopers (PwC) to carry out a report into the viability of keeping the ship as a tourist attraction in Leith.
The report, published in June, estimated the costs of doing so at were more than £10m, with a minimum of £4m ongoing operating costs.
The report stated that buying the ship would cost around £625,000, bringing it to the port of Leith around £440,000, and converting and restoring around £9.15m.
Three options were given: a standalone, separately-moored attraction, a joint facility run by the current management team of HMY Britannia, or one component of a larger-scale maritime attraction.
Even with ticket sales included, the report estimated that the attraction would operate at a financial loss.
It said: "On the basis of (the findings of the report) there does not appear to be any reasonable basis by which the public sector could support the project on value for money terms."
Lord Provost of Edinburgh Donald Wilson said: "I am obviously disappointed that we could not in the end bring HMS Edinburgh to the city, but the campaign to save HMS Edinburgh has not been in vain.
"Thanks to huge support from the local community, we hope a piece of her history will always remain in Edinburgh as we await a decision from the MOD on the potential for 12 artefacts taken from HMS Edinburgh to be gifted to the city."
"I thank the Ministry of Defence and the 'Save HMS Edinburgh' campaign group for their ongoing support throughout the council's feasibility study."
HMS Edinburgh, the last of the Royal Navy's Type 42 destroyers, came out of service on 6 June 2013. Type 42s are being phased out in favour of newer Type 45s.
The ship served in the 2003 Iraq war and underwent a £17.5m refit in 2010.
The "Save HMS Edinburgh" Facebook page, which has been operating since May 2013, has 2,372 likes. An e-petition to save the ship gained 2,867 signatures.