The former World Cup winner, Dunga, who was in charge of the Brazil national side from 2006 until his sacking in 2010, replaces Luiz Fellipe Scolari.
Scolari resigned in the wake of Brazil’s humiliating 7-1 semi-fimal defeat to eventual winners Germany.
50-year-old Dunga was sacked by the Brazilian Football Federation (CBF) after Brazil were knocked out of the 2010 World Cup at the quarter-final stage, but has been given another opportunity to lead his country.
The Brazilian football confederation confirmed the appointment at its headquarters in Rio de Janeiro.
Dunga, captain of the Brazil side that won the World Cup in the United States 20 years ago, was unveiled a press conference on Tuesday.
“I am immensely happy to be back,” he said.