Tuesday's hiring comes two weeks after Brazil was eliminated from the World Cup in a humiliating 7-1 loss to Germany in the semifinals.
The 50-year-old Dunga replaces Luiz Felipe Scolari, who resigned last week after Brazil failed to win football's premier event on its home soil.
It could be a difficult road for the former defensive midfielder. Several polls released in the last few days show he is highly unpopular, by margins of at least 3-to-1.
"When it comes to the survey, we have to overcome that," Dunga said. "I think they (fans) will eventually understand the work we are planning, and I don't feel rejected. ... I'm not going to change people's mind set, but I will change the way people think about me."
He also brought up the name of former South African President Nelson Mandela.
"Without firing a gun, he changed how people thought about him," Dunga added.
The Brazilian football confederation confirmed the appointment during a news conference at its headquarters in suburban Rio de Janeiro, but gave no details about salary. CBF President Jose Maria Marin indicated he wanted Dunga to continue until the 2018 World Cup in Russia.
Dunga gave a blunt evaluation of Brazil's situation.
"We're no longer the best," he said. "We're all aware of this. We can't tell our fans that we're the best."
Dunga came to the job for the first time in 2006 with no management experience. He was criticized for the team's physical style of play and conservative tactics and spent time Tuesday suggesting he might be different this time.
He said his focus was already on the next World Cup. Brazil will also play next year in the Copa America — the South American championship — and in a special Copa America edition in 2016 played in the United States.
"My first time as coach, I was asked to rescue the team's value and get results," he said. "This second time around, the focus is on preparing the side for the 2018 World Cup."
Dunga's real name is Carlos Caetano Bledorn Verri. His nickname Dunga literally means "Dopey" in Portuguese — the same as one of the characters in Disney's Snow White and the Seven Dwarfs — and was given to him during childhood because of his small stature.
He was the captain of Brazil's 1994 World Cup-winning team, and coached the national team at the 2010 World Cup in South Africa. He was dismissed after Brazil lost 2-1 in the quarterfinals to the Netherlands.
"He has shown his capacity to lead the Brazil team, not only in words but also in numbers, that he has all the requisites and the capacity to lead the Brazil team again," confederation president Jose Maria Marin said. "It was a decision made with the participation of everyone here at this table in a show of unity and total integration aimed at great conquests in the future."
Dunga's returned was linked to the naming of Gilmar Rinaldi as the new technical director, replacing Carlos Alberto Parreira. Rinaldi, who sat next to Dunga on Tuesday, was a goalkeeper on the '94 team and has recently worked as a player agent.
Dunga was in charge of 60 matches as national team coach in his first stint. Brazil won 42, drew 12 and lost six.
Brazil's image took a battering in the 7-1 loss to Germany. Many said it was worse than Brazil's 2-1 loss to Uruguay in the final game of the 1950 World Cup, which was played at the Maracana Stadium in Rio.
The loss against Germany broke several records and was one of the worst in Brazil's history. The loss was also the first in a competitive match at home since 1975.
Associated Press writer Jenny Barchfield contributed to this report.
Stephen Wade on Twitter: http://twitter.com/StephenWadeAP