Dunga, 50, led Brazil to World Cup glory as a player in 1994 and returns for a second spell as manager, having been dismissed in 2010 when the Brazilians were knocked out by the Netherlands in the World Cup quarter-finals.
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Scolari masterminded Brazil’s latest World Cup campaign but the hosts crashed out at the semi-final stage, hammered 7-1 by eventual winners Germany, and he subsequently quit his post.
A hard-working midfielder as a player, Dunga plied his trade in Brazil, Japan, Germany and Italy, and earned 91 caps for his country.
He was named manager in 2006 and led Brazil to glory in the 2007 Copa America and the 2009 Confederations Cup but they lost 2-1 to the Netherlands in South Africa four years ago, costing Dunga his job.
"I am immensely happy to be back," Dunga said on Tuesday. "Thank you for your confidence in me.
"The fans are very down right now but they are right behind the team. I am not here to sell a dream, we must get down to work."
Brazilian Football Confederation (CBF) president Jose Maria Marin is confident the re-appointment of Dunga will prove a success.
"He was world champion, captain of a world champion side," said Marin.
"He has what it takes to lead the Brazil team. The numbers show he absolutely has the ability to take charge."