The 57-year-old former Corinthians boss, whose full name is Adenor Bacchi, told a packed press conference in Rio de Janeiro that he was overcome with emotion, reports Xinhua.
"I called my mum this morning and told her, 'Your son is the coach of Brazil's national football team'," Tite said.
"She cried and gave me her blessing. Today somebody at the airport said to me that there are 200 million people supporting me. It makes my legs shake when I think about it. Even now I can really believe what is happening."
Tite replaces Brazil's 1994 World Cup-winning captain Dunga, who was sacked after the Selecao's group-stage elimination from the Copa America last week.
Tite is more concerned for Brazil's listless form in the 2018 World Cup qualifiers than the team's early exit in the Copa America championship.
The Selecao are currently sixth in the South American zone standings with just two wins from their first six matches.
Only the top four teams are guaranteed a place in the tournament while the fifth-ranked side will earn a playoff spot.
When asked if Brazil could miss out on a World Cup berth for the first time, Tite replied, "That's the reality and there is no escaping it.
"The current situation isn't great but we have quality players who, importantly, have potential to improve."
"I want the national team to start winning again and playing well. It will be a way to give Brazilian fans the joy that I'm feeling now."
Tite is regarded as one of the most successful managers in Corinthians' history. He led the Sao Paulo outfit to the 2011 and 2015 Brazilian Serie A titles, and the 2012 Copa Libertadores-FIFA club World Cup double.
Some observers questioned how Tite could accept the position barely six months after lobbying for the removal of Brazilian football confederation president Marco Polo Del Nero due to his indictment by the US department of justice on corruption charges.
Del Nero was the man, who offered Tite the Brazil coaching job last week.
"The invitation was to be coach of Brazil's national team," Tite said. "The best way I can contribute is by having the autonomy to do what I know best, always using transparency, democracy, excellence and modernity. That is what I can bring."
Among the most pressing challenges for Tite will be to revitalize captain Neymar, whose recent performances for the national team have been marked by ill-discipline and poor form.
"I can guarantee that Neymar wants the best for the team, just like everybody else. It's up to us to find the right path to get the best out of him," Tite said.