The 49-year-old, who has not coached since Brazil's quarterfinal exit at the 2010 World Cup in South Africa, replaces Fernandao, who parted ways with the club last month, reports Xinhua.
It marks a homecoming for Dunga, whose 20-year professional career began and ended with the Porto Alegre outfit.
"I never left Internacional, even after my playing career finished I have always been here as a fan," Dunga told a press conference Wednesday night.
"Working for this club is like working for the national team. It's not a matter of when you want it, but when you are called upon. Inter opened its doors to me when I was 14 years of age and now it's time for me to give something back."
Despite boasting a team that includes Uruguay international striker Diego Forlan and Brazil centre-forward Leandro Damiao, Internacional finished the 2012 Brazilian Serie A championship in 10th place.
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Dunga said plans were underway to bring success back to the club.
"We are building a team and evaluating players. (President Giovanni) Luigi already knows what I think," he said.