The brand-new stadium built at a cost of 592 million reais ($296.58 million) in the northern city of Salvador will be one of six used for the June 15-30 Confederations Cup, an eight-nation dress rehearsal for the World Cup.
Delays forced world football's governing body FIFA to extend the deadline for the first batch of stadiums until April 15.
Preparations for the tournament, and the Olympic Games in 2016, are behind schedule, raising doubts about the country's ability to organise the two global events that will draw hundreds of thousands of visitors.
Brazilian authorities, keen to avoid an international embarrassment, have doubled efforts to ready the stadiums and are optimistic they will be delivered on time for the June 15-30 warm up event.
"We are an unbeatable country. We will show that Brazil can deliver great quality to the Confederations Cup, the World Cup and the Olympics," Rousseff said at the opening of the Salvador stadium.
The Fonte Nova stadium was demolished and rebuilt from scratch after seven fans died when part of the terracing collapsed during a game in 2007. It will host three Confederations Cup games - Nigeria v Uruguay on June 20, Italy v Brazil on June 22 and the third-place play-off.
Police fired tear gas to quell a riot that broke out last week when tickets went on sale at the Salvador stadium, and several fans were hurt in the incidents.
The Arena Pernambuco stadium will be inaugurated on April 14 and the Mane Garrincha National Stadium in Brasilia will open a week later, less than two months before the Confederations Cup kicks off there on June 15 with Brazil facing Japan.
To standardise names and make it easier for foreign fans buying tickets, FIFA will shorten its name to National Stadium Brasilia, dropping the name of the football great Mane Garrincha, star of Brazil's 1962 World Cup victory, a city official said.
The last stadium to be ready will be the Maracana in Rio de Janeiro, once the world's largest but now overhauled to fit a reduced capacity of 78,639 spectators. It is due to be delivered on April 27.
