The ban "concerns all species of elephant and rhinoceros", Royal said in a statement Wednesday, although special exemptions may be granted.
And it does not forbid the possession of ivory and rhinoceros horn.
Many private individuals and museums own artefacts made from ivory, some of considerable age.
With African and Asian elephant populations threatened by the slaughter of animals for their ivory, a worldwide ban on the trade came into effect in 1989, but it did not cover the sale of ivory obtained before that date.
Poaching of elephants and rhinoceroses, whose horns are used in traditional Chinese medicine, has continued and the populations have continued to decline.
Royal announced that she meant to introduce a ban in April when she watched the destruction of 105 tonnes of ivory as part of a government campaign to stamp out poaching, an example France followed in 2014.
In July a position paper by the European Commission opposed a total ban the ivory trade, arguing that it would better for countries with growing elephant numbers to "sustainably manage" populations.
Arctic visit to monitor climate change
Royal, who is also responsible for France's international relations on climate change, was to leave Paris for Oslo on Wednesday on her way to the Arctic archipelago of Svalbard.
There she will visit the Emile Victor French Polar Institute, the home of a joint research programme with Germany.
As well as observing the melting of the polar ice cap, she will be able to see more endangered species, including whales, seals and polar bears whose survival is threatened by global warming.
To read our coverage of the 2015 Paris climate change conference click here