The museum will display indigenous art from Africa, Asia and Australasia.
It is the first major museum to open in the French capital since the Pompidou Centre in 1977.
But the project has been controversial. It opens as France debates how to heal the scars of its colonial past and accept a multi-ethnic nation.
Critics say the museum does not do enough to explain to visitors the damage done by colonialism to many of those cultures.
The Musee du Quai Branly, on the banks of the River Seine, has been a decade in the making.
It combines angular glass walls with futuristic cubes of bright colour and, outside, a green wall of thick vegetation, suggestive of a forest or a jungle.
The museum was designed by French architect Jean Nouvel, and is meant to be President Chirac's legacy after nearly 12 years in office.
But behind the leafy exterior, visitors may be surprised to find, not classic French artists, but artefacts from Africa, Asia and Australasia - from masks and spears from Papua New Guinea to costumes from Vietnam and Thailand.
Its curators insist the museum is a celebration of cultural diversity, a way of showing how Europe has interacted with other civilisations.
However, critics on the left in France say that it is more typical of the nation's reluctance to face up to the


