Dunga, whose real name is Carlos Bledorn Verri, previously coached Brazil from 2006 to 2010, where he won the 2007 Copa America and the 2009 Confederations Cup.
He was fired by the Brazilian Football Confederation (CBF) after losing to the Netherlands in the quarter-finals of the 2010 World Cup.
Dunga replaces Luiz Felipe Scolari in the job.
Scolari, who guided Brazil to their fifth World Cup title in 2002, resigned as coach after the 2014 tournament where the hosts entered as hot favourites but finished fourth.
They were also humiliated by eventual champions Germany 7-1 in the semi-finals and then lost the third-place playoff 3-0 to the Netherlands.
Dunga's last job was as coach of Internacional, where he spent a great part of his playing career, but was sacked last October after a fourth successive loss in the Brazilian league that left them mid-table.
As coach of Brazil's national team, he led the team to 42 victories, 12 draws and six defeats.
- Sports & Recreation
- Luiz Felipe Scolari
- 2010 World Cup