Square roots: Artist Donald Judd's New York apartment opens its doors to the public

It's time to reappraise the artist's work in the context of his home, says Charles Darwent.

Rainer Judd and I are lying on what she calls "the make-out bed", a piece of furniture designed for the space by her father. This might be alarming, were Rainer not young and beautiful and I… Well. She is snapping me on my iPhone, a thing she does deftly and crisply, a sign of her career as a film-maker.

"OK, lie back and… no, further back. Like that," she says, clicking a few more times and then handing over the phone. The images are grimly true-to-life. "You see? People say that my dad's furniture is uncomfortable, but that's because they've never had a chance to use it," Rainer enthuses. "They've never sat on one of his chairs, or spent a whole day lying in this bed."

It is, for various reasons, unexpected. Rainer Judd's father, the one who made the bed, was Donald Judd, a man commonly described as a "minimalist sculptor", although he denied that his work was either sculpture or minimal. You can see several of Judd's "specific objects" (or, sometimes, "discrete objects") at Tate Modern, among them Untitled (1972), an open-topped copper box a metre or so high by two wide, anodised on the inside with a red aluminium gloss.

When this was made, Judd was living here at 101 Spring Street in New York's SoHo – an acronym (SOuth of HOuston Street) he also disliked on the grounds that it sounded like London. The house, a five-storey, cast-iron structure, was the first he owned, bought cheaply in 1968 as a home for his family before he moved them to Texas a decade later. The foundation Judd set up there, in a half-horse town called Marfa, has become one of the sacred places of modern art, visited by pilgrims hardy enough to brave the road from El Paso.

Spring Street, though, has stayed more secret, although Judd owned the house until his death in 1994 and lived and worked there when he was in New York. Now, after a three-year restoration, it will open to the public.

It may redefine Donald Judd as an artist. Visit Marfa and what you see, or think you see, is an urban taste superimposed on the country. There are, most obviously, the half-mile sequence of Judd's concrete boxes marching across Marfa's scrubby fields and his 100 polished aluminium boxes in a glass-sided shed. These last are sublimely beautiful, changing as the sun moves, turning black or glassy or glowing suddenly like flame. They are not domestic, though – and certainly not comfortable.

Which brings us back to Spring Street and the bed. As Rainer Judd points out, this is comfortable, though it doesn't look to be. It looks like a Donald Judd – an unadorned wooden box, open at the front, bigger than the Tate's Untitled, but with similar proportions.

Both are very like the specific object that sits on the floor of Judd's studio, one storey up. It seems hard to believe that this work is here, in a room in a house in a city. Another box, open-sided this time, the piece is huge – perhaps 1½m high by 3m deep and made out of 5cm-thick steel plate. What it weighs or how it got there is anyone's guess. "I spent a lot of my childhood running through boxes like this," remarks Rainer Judd, thoughtfully. "If they were steel or concrete, that was fine. If they were plywood, though, no."

And suddenly, a long-time fan, I see a new Donald Judd. His writings, like his work, are pared-down and clever. Many are to do with the relationship between the space objects occupy and the architecture they sit in. These things have seemed hypothetical, the output of Judd's huge brain, his training as an art historian with two of the subject's great names, Rudolf Wittkower and Meyer Schapiro. Now, they show a different Donald Judd: emotional, human and humane; a Judd who begins at home.

"When Jamie [Dearing, Judd's long-time assistant] first saw this piece here, he said, 'Oh, so that's why you needed Marfa,'" Rainer recalls. He was right. Her father had to measure his objects against a bigger space than SoHo allowed – the West, the desert, the sky. The impulse to do so, though, begins here in this house. It starts, maybe, with the piece over Judd's bed on the top floor.

It isn't the most eye-catching of the works in the room – these including a wall-length Dan Flavin light installation and a crushed-car piece by John Chamberlain. (Judd, a good friend, gave both their own spaces at Marfa.) It is an early work, from the days when he had just moved from painting to object-making – shallow, hung on the wall like a canvas although it is actually a wooden box. The real thing about the piece, though, is that it was made by Donald's father, Roy, a man good with his hands, the last of a line of farmers and craftsmen. For all its hard edges, it is, unexpectedly, a story of love.

A selection of Donald Judd's work, including pieces made at 101 Spring Street, will be on show at the David Zwirner Gallery, 24 Grafton Street, London W1 (020 3538 3165) from 21 June to 3 August. To book a guided tour of the house: juddfoundation.org