Organisers have pulled the plug in the face of ongoing uncertainty over what Covid restrictions will be in place in Scotland later in the summer.
Work had been expected to get underway this month on the for the event and talks had been ongoing with the city council about building smaller-scale spectator stands.
However Tattoo chiefs said it was clear that the financial risks involved in pressing ahead with the event were “simply too great.”
The said it would have been “irresponsible” to risk the long-term viability of the event, which has been unable to secure insurance to help pay for the increased costs of an eleventh-hour cancellation once the arena was in place.
The Tattoo had been expected to get the green light to go ahead from the Scottish Government and the city council as a signature event for the country and its international reputation.
However the government has refused to drop an insistence that all events planned later in the year must go ahead with two metre social distancing.
First Minister Nicola Sturgeon has been warned that the restriction – which compares to 1m distancing in bars and restaurants – would make the vast majority of events unviable.
The Tattoo launched ticket sales last October in the hope that it would be able to go ahead at around half its normal capacity if distancing restrictions were still in place.
However an ongoing review of the future of social distancing in Scotland is not expected to be known until early next month.
The Tattoo which has been staged at Edinburgh Castle esplanade since 1950, is thought to be worth more than £100 million to the economy.
Tattoo chief executive Buster Howes said: “Despite the sense of optimism around the UK’s emergence from the Pandemic and our huge enthusiasm to stage a performance this year, it is now clear that the financial risks we confront in delivering The Royal Edinburgh Military Tattoo at scale, on the castle esplanade in August are simply too great.
“We have for months forensically monitored, assessed and sought to mitigate the constraints and uncertainties involved in mounting our show.
"However, we now reluctantly conclude it would be irresponsible to press on and risk our longer-term financial viability, without the ability to underwrite and to offset the potential, substantial economic losses associated with last-minute cancellation obliged by changes in public health policy.
“This has been a very difficult decision. We appreciate it has far-reaching implications for our staff, performers, suppliers, and guests, but we must act responsibly and, in the best, long-term interests of all.
"Tickets for 2021 will be refunded in full. For those wishing to join us next year, tickets can be transferred to 2022.”
A government spokeswoman said: “We don’t underestimate the severe impact this pandemic has had on large-scale events and completely understand the very difficult decision the Tattoo has had to take.
“We've been working closely with the organisers to fully explore the possibility of delivering the Tattoo this year, including supporting the implementation of Covid-19 measures and offering clinical advice.
"We’ll continue to offer support to ensure this internationally significant show can build on its longstanding success and iconic status, and return next year.”