How long does it take an artist to become a national treasure? In Antony Gormley’s case, the process began when he got schoolchildren to make endearingly primitive clay figurines for his Field series, and concluded with his Angel of the North. This makes him our unofficial sculptor laureate. The latest candidate for national- treasure status, however, is more unexpected: the hirsute Arizonan rancher-pilot-artist James Turrell.

No less august a body than the National Art Collections Fund (which these days likes to call itself the Art Fund) has splashed out £800,000 to build a permanent Turrell Skyspace in the pastoral setting of the Yorkshire Sculpture Park (YSP). So excited is the fund by this, its centenary project, it has been moved to hyperbole. This, it states, is its “most significant gift to the nation since The Burghers of Calais by Rodin in 1911”.

I don’t know if Britain had many other Rodins knocking about in 1911, but Turrell, who would win any ZZ Top lookalike contest, is certainly no stranger to these shores. Indeed, his Skyspaces — contemplative rooms that frame the sky, allowing you to sit and, um, look at the sky — have become a bit of a production line. They are all over the world, and are already in Britain. He did one in Cornwall, the Elliptic Ecliptic, for the solar eclipse of 1999. A related Turrell project, a light installation, was the centrepiece of the Dome’s Faith Zone.

Subsequently, he was commissioned by the Kielder Arts Trust to build one high on the Northumberland moors. It is in a remote location, requiring what amounts to an act of pilgrimage to get to. Reader, I have made that pilgrimage. When you finally find it, sunk into the landscape, you will have yomped along steep forest tracks for miles. I have to report that, despite apparently being the only circular example in the world, it is more than somewhat disappointing. A bit of sky, eh? Would that be the same sky you have been very much aware of all the way there?

Of course, Turrell’s point is that it is not just the same bit of sky, or even a different or ever-changing bit of sky. His art is about the act of seeing rather than the thing seen. In all his light- and space-based art, we are experiencing our own perceptions. Making a mystical experience out of what is essentially an open skylight is all about removing distractions, taking time out, letting your thoughts fly free — yeah, all that hippie stuff. Here’s the good news: the Art Fund has not wasted its money. The new Skyspace in Yorkshire works for me in a way that the Kielder example does not.

It is hard to say exactly why, as the principle is the same in all cases. But each Skyspace responds to its circumstances in subtly different ways. At the YSP, Turrell has commandeered an existing landscape building, the listed 18th-century Deer Shelter, which takes the form of a walled sunken pen, backed with a row of deep brick arches built into the hillside behind. What he has done is to convert the Deer Shelter into the entrance to his Skyspace, making it a threshold to another world.

Achieving this was quite some task, one that involved excavating 2,000 tons of rock and soil, then putting 370 tons of concrete and steel back in. The result is a part-buried chamber, 29ft square and 24ft high. For all its size, it does not impinge much on the landscape. You enter the pen through a rustic gate, pass through a doorway at the back of the shelter, find yourself in a low, narrow vestibule and emerge into the light-drenched space.

This not-quite-exact cube has the usual bench seat around the walls, here done rather sumptuously in polished concrete (heated in cold weather), with a tall, angled back rest. The walls and ceiling are white, and there is the usual sharp-edged opening to the sky. As well as the heavens, you witness the sundial effect of the patch of sunlight projected by the aperture moving across and down the wall as the day progresses. Or, of course, you might get an overcast day where nothing much happens except the flickers on your retina.

It works better than Kielder because, apart from the coup de théâtre of the entrance, it is larger and better proportioned. It had a bigger budget, and Turrell has used it well, making a nobler space. He famously had a Quaker upbringing, and explains much of his work in terms of his grandmother’s injunction to “go inside and greet the light”, but this feels somehow priestly, even Egyptian.

You sit there, put your mind into neutral, watch the sky and the scudding clouds, observe the odd bird and bee traverse your line of vision, and realise that this is not just a light-and-space sculpture. It is also a sound piece. It appears to capture the background noises of the park — birdsong, the roar of wind in the trees, distant voices — which become the disembodied soundtrack to the vision thing. It captures that sense of clarity and distance you sometimes get at the point of falling asleep. It is vaguely hallucinogenic.

So it seems there is life in Turrell’s Skyspace series yet. Perhaps the way to see them is as cosmic phenomenons, satellites of his life’s work: the Roden Crater project, in the Arizona desert, where he is creating an art synthesising land and sky on a scale comparable to the puzzling earth- marking of ancient civilisations. Seen this way, each Skyspace is not so much an entity in itself as an outlier of the mother project. My only reservation is that the YSP is getting to be a popular place; and, unlike remote Kielder, this Skyspace is rather too easy to get to, near the entrance. Being in there alone is one thing. Being there with gaggles of shouty kids on a day out from Leeds will be quite another.

So, is this really as significant a gift to the nation as Rodin’s Burghers of Calais in 1911? Probably not. But it merits the detour.

The Deer Shelter Skyspace opens on Friday at Yorkshire Sculpture Park, Wakefield