The Porto Alegre club confirmed the appointment on their website (www.internacional.com.br) on Wednesday and said the 49-year-old would be officially presented at 1700 local time (1900 GMT).
Dunga coached Brazil for four years, winning the Copa America in 2007 and the Confederations Cup in 2009.
He was appointed in 2006 to succeed Carlos Alberto Parreira, despite having no previous coaching experience at senior level.
Under his leadership Brazil developed a physical, counter-attacking based game which was unpopular with many fans and their World Cup campaign ended with a 2-1 quarter-final defeat by the Netherlands.
As a player, Dunga was a feisty, defensive midfielder with a spiky haircut and almost permanent snarl who played in three World Cups, captaining the side who won the tournament in 1994.
His club career started and ended at Internacional and took him to Corinthians, Vasco da Gama and Santos in his homeland, Pisa, Fiorentina and Pescara in Italy, VfB Stuttgart in Germany and Japan's Jubilo Iwata. (Reporting by Pedro Fonseca; Writing by Brian Homewood; Editing by Julien Pretot)