The 49-year-old, who both started and finished his playing career at the Porto Alegre-based club, will be officially presented at a press conference today, Internacional announced on their official website. He replaces Fernandao, who left the club last month.
Dunga made 91 appearances for Brazil and captained the side that won the 1994 World Cup in the United States.
In 2006 he took over as Brazil coach - his first coaching position either at international or club level - and won the Copa America in 2007 and Confederations Cup in 2009.
He stepped down following the 2010 World Cup in South Africa, where Brazil were eliminated at the quarter-final stage by Holland.
As a player, the defensive midfielder played for a host of clubs in his homeland and in Europe, including Corinthians, Santos, Pisa, Fiorentina and Stuttgart.
Dunga also spent three years at Japanese club Jubilo Iwata before returning to his first club Internacional prior to hanging up his boots.