The authorities say that deforestation has been reduced due to greater controls on illegal logging, improved certification of land ownership and more initiatives to preserve the forest.
Marina Silva, the environment minister, told a news conference in the capital Brasilia: "It's a great achievement for Brazilian society. It reflects a new environmental governance."
But environmentalists say deforestation has slowed largely because of the strengthening of Brazil's currency and a drop in the price of soybeans, which makes it less profitable to clear forest to grow the crop.
Paulo Moutinho, of the Environmental Research Institute of the Amazon, said: "Awareness and policies improved in the federal and state governments, but the real test is if rates fall during a commodity price rally."
He added: "I'm optimistic but it's too early to celebrate."
Brazil has often been accused of allowing its farm exports to contribute to destruction of the Amazon.
The government under Luiz Inacio Lula da Silva, Brazil's president, has increased police raids on illegal logging and expanded protected areas.
At the same time, though, it has built roads and hydroelectric plants in the region, which conservationists fear could increase deforestation in the long term.