Alison Watt could be forgiven for feeling a little tired today. For the past two years she has been artist in residence at the National Gallery in London and, in the build-up to the opening of her new solo show, Phantom, has often been working seven days a week. Last night she finally unveiled the seven new, large works - which have already been described as proof that painting is not dead.

The past two years have been life-changing for Watt. "It has been an extraordinary experience," she says, "and I really don't know what I am going to do next."

As well as feelings of exhaustion, Watt, who was born in Greenock and is a graduate of Glasgow School of Art, also admits to feeling a little sad that her time at the gallery is coming to an end. "I feel quite emotional, because it's a letting go of what I have been working on for two years. I have been getting lost in the work, and now finding myself is quite hard."

Watt's new works were inspired by her immersion in the collections of the National Gallery - in particular, what she describes as her "obsession" with Saint Francis in Meditation, the masterpiece of sacred art painted by Francisco de Zurbaran. She returned to the painting day after day when she was working in the gallery, and the "points of entry" in her new pieces were partly inspired by the dark shadows of the saint's eyes and mouth.

Saint Francis in Meditation depicts the hooded saint kneeling in semi-darkness. "There is something weird about that painting," says Watt. "It is about what you don't see as much as what you can see. I've become obsessed with the picture, and a huge part of that painting is the open mouth; it is the key to the painting, along with the gaping hood, the bowl, the barely visible stigmata on the back of the hand. In a sense, negative spaces are the subject of that picture, that strange darkness, and the apertures have become the focus."

Watt called her exhibition Phantom because it is about "something you cannot quite pin down. It is something and nothing, all there at the same time. This is a different show, because it is about relating with great paintings," she says. "At the beginning of working with the National Gallery, I didn't know how to start. But you learn that creating something comes from fear, the fear of not doing anything. You have to make yourself make the first mark, and then the work comes from that. I have worked long periods on big projects, but nothing like this."

The exhibition is being held in the Sunley Room at the National Gallery, and contains Watt's seven new works - Pulse, Root, Echo, Vowel, Host, Eye and Phantom - as well as Zurbaran's Saint Francis.

Like much of her recent work, the new pieces are based on the folds and creases of fabric and material. Although the huge paintings might all look pale and overwhelmingly white to the casual onlooker, Watt painted them - often using a stepladder and scaffolding - with grey, sienna, cadmium red and yellow ochre.

Two of the new works have already been sold: one to the banking organisation HBOS for the company's headquarters in Edinburgh, the other to the British Council. Florence Ingleby, director of the Ingleby Gallery in Edinburgh, which represents her, says it is hoped the rest will be sold to public collections.

Many in the art world believe the new show could mark Watt's move to being recognised as a significant artist not just in Scotland and the UK but internationally. Several public art galleries hold work by Watt, including the Kelvingrove Art Gallery in Glasgow and the National Galleries of Scotland, but it is now believed her stock will rise hugely in Europe and the US.

The National in London has always been a special place for the artist - she was brought there as a child by her father, James, a landscape painter, and became fascinated with the portrait of Madame Moitessier by the French neoclassical painter Ingres, a key inspiration in her work. She now holds the distinction of being the youngest artist in residence in the gallery's history, as well as the first Scot.

Watt, who graduated in 1988, first gained public recognition when she won the John Player Portrait Award and was commissioned to paint the Queen Mother. Her next notable work, in 1997, included paired nudes in draped fabric thought to have been inspired by Ingres. This groundbreaking exhibition at the Fruitmarket Gallery, Edinburgh, led to a solo show at the National Gallery of Modern Art in Edinburgh in 2000; she was the youngest person to have been offered such a show. Entitled Shift, it featured a dozen large paintings made with fabric. At the Edinburgh Festival in 2004, her acclaimed work Still was hung in Old St Paul's Church on Jeffrey Street, and it was this piece that led to her becoming artist in residence at the National in London.

At first glance, her subsequent Dark Light, in 2007, appeared to be a dramatic departure from her previous work. It comprised a large, featureless metal cube, and visitors to the gallery were invited to step inside for at least 10 minutes. Once their eyes adjusted to the darkness, they could see that the walls and ceiling of the cube were images of exquisitely rendered folds of deep black cloth in Watt's trademark style.

She is a former artist in residence at the Glenfiddich distillery on Speyside and a winner of the National Portrait Gallery's portrait award; in 2003 she also won a Creative Scotland award. She was awarded an OBE for services to art at the beginning of this year.

"She works in the tradition of painting drapery, which has an established place in art," says Colin Wiggins, the head of education and a curator at the National Gallery, "but it is always a support, in the background as a rule. But she has brought it to the foreground and given us all kinds of new possibilities.

"I am still taking this exhibition in, but I think she has surpassed all her previous work here. My view is that she has moved to another level in the world of art, and I believe she now needs to be seen on an international platform."

Ingleby agrees. "It depends what she wants to do next, but I think she can go in many different directions. I really think she will now be picked up by galleries abroad. But it is an amazing achievement to have a solo show at the National Gallery in London."

Watt is not thinking about her next project. "All I have been doing is thinking about now, and my head is so tight and I have been so anxious about this exhibition that I've felt so exposed. So I don't know what I'm doing next. I cannot paint straight away, because it will just be a parody of what I have done here."

She does, however, have the use of the studio at the gallery until June. "It seems crazy not to use it, so I will continue to do so. London is meant to be about all the hell of getting around the city, so being in such a central position and being able to walk to Tate Modern has been so precious."
The exhibition runs until June 22, and admission is free.