Anders Holch Povlsen purchased the land and associated properties from Xavier-Louis Vuitton, heir to the French fashion label.
The latest acquisition by Mr Povlsen, who already owns the Glenfeshie, Ben Loyal and Kinloch estates, has increased the 43-year-old's land portfolio in Scotland to around 150,000 acres. It is second only to that of the Buccleuch Estates, with an estimated 280,000 acres.
Mr Povlsen, whose family owns Bestseller, the Danish fashion company that last year had a turnover of £2bn, also has substantial farming interests in his home country and owns areas of forestry in Romania.
He has been criticised in some quarters for mounting a "land grab" of Scotland to take advantage of farming subsidies, though others claim he is motivated by a desire to protect wild land.
His management of Glenfeshie is generally regarded as good, and he has overseen the regeneration of 1000 acres of woodland, including Caledonian pine.
However, the acquisition has dismayed some land reform campaigners.
Writer and commentator Andy Wightman, author of Who Owns Scotland, said: "Scotland has no coherent policy on land ownership, occupation and governance. I'd like to see an end to the unregulated market in this country, where anyone from anywhere can buy land.
"Estates like Gaick simply don't exist in the rest of Europe. In Norway, for example, which is seven times larger than Scotland, there are only 23 estates bigger than 10,000 hectares; in Scotland, there are 144.
"We're unique in having such large estates. Add to that the fact that the law is not regulated, and you have a recipe for dramatic changes in ownership, which can lead to disruption and uncertainty."
Rob Gibson MSP, a member of the Scottish Government's Land Reform Review Group, told The Herald: "The UK is one of the last countries in the world where you can buy land on this scale, and it's high time this was addressed. If you live in Denmark, you can't own more than 250 hectares of agricultural or forestry land, so for those who are rich and want to buy more land, this is their kingdom.
"It will be interesting to see what plans this gentleman has in terms of biodiversity and the local community. Some estates are used as private kingdoms by their owners, where the locals have absolutely no say. Mr Povlsen and others like him should be made accountable to their local communities."