The architect Frank Gehry has finished his first building in Britain - a cancer centre he designed for free.

In a remarkable project, some of the best-known names in architecture have also agreed to waive their fee and design similar centres around the country in tribute to a Scots architect who died of breast cancer.

Gehry's dramatic building, covering about 200 square metres, is at the Ninewells Hospital in Dundee and was commissioned by Maggie's Centres, a pioneering cancer support organisation.

It has the signature features of Gehry, who designed the spectacular Guggenheim museum in Bilbao, northern Spain. None of the walls in the £1.3m building is straight, and it has a concertina roof, made of stainless steel and timber, on which no two pieces are the same size.

Several of the world's other leading architects have submitted designs for the 10 further Maggie's Centres that are planned, including one each in Oxford and Cambridge.

Daniel Libeskind, recently chosen to rebuild on the site of the World Trade Centre in New York, has produced designs for a centre at Addenbrooke's Hospital in Cambridge.

Zaha Hadid - touted in some quarters as the new Gehry - is designing a centre at the Victoria Hospital in Kirkcaldy, Fife, with work due to start later this year.

Richard Rogers is designing Maggie's London, at the Charing Cross Hospital, and Piers Gough is creating a centre in Nottingham.

The organisation was founded by Maggie Keswick Jencks, a Scottish architect and landscape gardener. She and her husband, Charles Jencks, an American-born landscape designer and architectural writer, became friends with Gehry in California when Jencks was teaching at UCLA.

The couple later designed some spectacular gardens with sculptural mounds and lakes at their estate in Dumfriesshire. Jencks's other home in central London is also renowned for its interior design.

Maggie Keswick Jencks died from breast cancer in 1995, but she had already developed a blueprint for the centres. The first one opened the following year in Edinburgh, at the Western General Hospital, and another followed in Glasgow.

Gehry had asked Charles Jencks to contact him if he could help and he became a patron of Maggie's Centres. He was approached when Dundee was first mooted and the centre will open next month.

Although now 74, Gehry is still has a reputation as one of the world's most ambitious architects. He lives in California but has made several site visits to Dundee.

A series of elaborate models were sent over from the United States, and Gehry travelled to Scotland to liaise with a group of architects based in nearby Glamis, who were involved with the day-to-day work. Because of the way the steel roof has been laid, the constantly changing sky produces a myriad different colours - blue, grey and silver - as the clouds pass overhead.

The building, sitting on a slope, also has a central tower, resembling a lighthouse, which offers spectacular views across Tayside. The gradation of the roof concertina towards the tower is reminiscent of waves hitting rocks. Its lower floor is a library and the upper storey has a sitting-room. The rest of the open-plan building has a living room and kitchen, as well as a central entrance hallway and dining area.

Looking up at the inside of the roof, every piece of timber has been hand carved, and angles and pitches constantly vary.

Charles Jencks said: "The care and attention which Frank has given to designing Maggie's Dundee provides the perfect setting for the pioneering cancer support programme that will help 12,000 visitors a year".