She said the Games would bring "honour and pride" to the country.
Ms Rousseff, who has seen her popularity plunge amid a serious economic crisis, says the country will rise to the challenge and will organise a safe and successful Games.
She said 12,000 people would be chosen to carry the Olympic torch through some 300 Brazilian cities next year.
"We are now 399 days from the opening of the Olympic Games and on August 5 the whole world will look at us, will see the Olympic flame light up," Ms Rousseff said at a ceremony in Brasilia.
The torch relay will begin in the Brazilian capital in May and will end at Rio's Maracana stadium in August, at the Olympic's opening ceremony.
The Olympics organising committee and sponsors will choose the torchbearers in the next few months.
Each person will carry the torch for 300 metres.
The relay will take the torch through the Federal District, where Brasilia is, and 26 states during 90 to 100 days.
Ms Rousseff has promised security will be a priority, inviting the thousands of fans who travelled to Brazil for the football World Cup to return for the Rio Games.
Members of the International Olympic Committee have expressed concern over delays in the works for the Games.
Another major concern has been pollution in the waters of the Guanabara Bay, where the sailing and windsurfing events will be held.
The authorities say they understand athletes' concerns but insist that water pollution will not pose a major health risk during the Olympics, which will be held in August 2016.
"We are confident that we can meet the challenge before us," said Ms Rousseff.
"We will put on a historic Olympics."
Rio de Janeiro will be the first South American city to host the Olympics.
Brazilian President Dilma Rousseff has unveiled the torch to be used at the 2016 Olympics in Rio de Janeiro.