Go Ape said it could no longer operate at Crathes Castle near Banchory given the extent of the damage to the site last November.
The adventure playground, where users navigate the woodland at height on a series of zip wires, rope bridges and swings, opened at the castle in 2011.
Since the storm five months ago, attempts have been made to find an alternative spot for the adventure park in the castle grounds, but no suitable location could be found.
Iain Hawkins, the National Trust’s general manager for the North East, said: “It’s with great sorrow that we’ve been informed of Go Ape’s intention to vacate the grounds of Crathes Castle.
“Unfortunately, we must face up to the reality that this winter’s violently destructive storms have damaged the northern segment of the property’s woodland, where Go Ape is located, to such an extent that the attraction is no longer viable.
“We did look for potential alternative locations within the grounds but, unfortunately, there is nothing suitable and we have to bow to the inevitable. It’s a real shame, as Go Ape attracted so many visitors, especially young people, and we will always be grateful that the partnership was so successful for so long.”
Go Ape runs similar sites at Aberfoyle in the Trossachs, Glentress Forest in the Borders and Dalkeith in Midlothian.
The company said it would “fondly remember” its time in Deeside.
In a statement, the company said: “The adventure is over. Sad news. Our forest doors at Crathes Castle have closed for good.
“Storm Arwen left her mark in November 21 and our course received significant damage.
“It’s been an adventure and one we’ll fondly remember.”
Storm Arwen damage may cost £300m
NTS properties were particularly badly hit by the storm, which lashed North East Scotland and England with winds peaking at more than 90mph.
The conservation charity estimated that up to one million trees on it estate were either damaged or destroyed by Storm Arwen.
Up to 100,000 trees were blown down at Haddo House near Tarves in Aberdeenshire alone. A further 200 trees came down at Castle Fraser near Sauchen with Leith Hall at Kennethmont also badly hit.
Paths throughout many grounds remain closed with a mass replanting program now being drawn up at the trust.
Many of NTS’s estate woodlands in the North East were planted following another extreme rare weather event – the Great Storm of 1953.
As a major landowner at the time, NTS embarked on mass replanting with Sitka spruce, Norway pine, larch and Scots pine taking root.
In many cases, it is these trees, now matured, that came down during Storm Arwen last year.
Meanwhile, one insurance company said it had received claims worth more than £80m following Storm Arwen, with 8,000 separate claims made.
The total cost to insurers has been estimated at between £250m to £300m.
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