The museum is seen as Mr Chirac’s architectural and cultural legacy to the French capital.
The Musee du Quai Branly is housed in a contemporary building designed by the architect Jean Nouvel on the banks of the River Seine.
The collection brings together about 300,000 objects from Asia, Africa, Australia, the Pacific and the Americas.
"France is paying homage to the peoples who, throughout the ages, history has often treated with violence ... to the peoples brutalised and exterminated by greedy and brutal conquerors," Mr Chirac said as he unveiled a plaque.
"At the heart of our move is a refusal to be ethnocentric, a rejection of this unreasonable and unacceptable claim that the West is the sole carrier of humanity's destiny."
In a world of globalisation "this diversity is a treasure which more than ever we need to preserve," he said.
The museum, costing A$386 million dollar, is Mr Chirac's legacy to the city in the final year of his presidency.
The legacy is a tradition among outgoing French presidents. Mr Chirac’s predecessor Francois Mitterrand gave Paris the Louvre pyramid among other works.
Mr Chirac conceived the museum eleven years ago and is the first to be opened in the French capital since the Georges Pompidou Centre in 1977.
UN Secretary General Kofi Annan was among the guests at the opening along with the Guatemalan 1992 Nobel Peace Prize winner Rigoberta Menchu, the premier of the Canadian territory of Nunavut, Paul Okalik, French Prime Minister Dominique de Villepin and Australian Foreign Minister Alexander Downer.
"In a world in search of its reference points and its values, museums such as this one are places where humanity conserves and rediscovers confidence in itself," Mr Annan told the inauguration ceremony.
Sanctuary for tribal arts
The bulk of the collection, of which some 3,500 objects will be on permanent display, has been drawn from two existing Paris collections previously housed in the Musee d'Homme and the Museum of African and Oceanic Arts.
"We are the keepers and the guardians of these pieces. Their history is much longer than the history of the museum," the museum's president Stephane Martin said.
Architect Jean Nouvel said he had wanted to create a sanctuary for the collections of tribal arts, which in the past have been dismissed by many as not worthy of being called art.
"We have tried to build them a home, and this is a respectful and spiritual house where the objects are still alive," he told AFP.
But many of the objects were collected by explorers, missionaries and travellers during France's colonial years, and at a moment when France is still struggling to come to terms with its colonial past and its impact on the country today, the museum is certain to fuel a debate.
Some experts have argued that such works should be rightfully restored to their countries of origin.
"Should all Italian paintings go back to Italy? Should all Spanish paintings go back to Spain? I think there would be a cultural impoverishment in the world," said Mr Martin.
The objects are grouped according to continent, and have been displayed in a world of shadows, light and reflection, so that in some cases one window of objects is seen reflected in another.
The central permanent exhibition has a huge six-level glass-fronted column descending through the building at one end, housing the museum's reserve of some 9,500 musical instruments.
Rarities include a wooden duck from Papua New Guinea which is pounded onto water to create a sound, and a wooden block only found in New Ireland province in PNG that vibrates when the musician rubs his resin-smeared hands over it.
Some of the objects on display have retained their mystery, such as a long Polynesian wooden staff topped with a kind of shelf which experts believe was used for holding offerings during religious ceremonies.
In the next window are 19th-century stilts used in sports by young men in the Marquesas Isles, while across the way are wooden pillows and intricate fans woven out of coconut fronds.
"I knew these collections separately, but it's wonderful to see them reunited like this," said Oceanic specialist Magali Melandri.