The 48-year-old, currently coach of Corinthians, confirmed he had said yes to the Brazilian Football Confederation (CBF), which had been turned down by Muricy Ramalho on Friday when his club Fluminense refused to release him.
"For the whole of Brazil, I say that I officially accept the invitation," Menezes told a news conference at his club. "I'm very proud and happy."
"We must have 30, 40 or 50 excellent professionals in Brazil, so if I'm second on the list, that's fine by me."
Menezes replaces Dunga, who quit after Brazil's shock quarter-final defeat to Netherlands at the World Cup three weeks ago. Both men hail from the south of Brazil, regarded as the more European part of the country.
Menezes, who did not play professionally, will have the huge task of trying to rebuild Brazil's national team, discredited after a lacklustre display in South Africa, and win a sixth world title when they host the 2014 World Cup.
Winning their own World Cup is seen as an obligation by Brazil's 190 million inhabitants. With Brazil's failure to win on home soil in 1950 still being mentioned regularly, the pressure on Menezes and his team will be greater than ever.
He will also be under pressure to restore a more attractive playing style which many felt was missing under Dunga's leadership.
FRIENDLY MATCHES
One of his biggest problems could be that Brazil will qualify automatically as hosts and will be short of competitive football, with only next year's Copa America and the 2013 Confederations Cup to test the team.
Otherwise, he faces a long run of friendlies, starting with a match away to United States on August 10.
Menezes, 48, made his name in 2005 when he led former South American champions Gremio out of the second division.
In an extraordinary decisive game, Gremio had four players sent off, survived a penalty miss by opponents Nautico and then snatched a goal to win 1-0 and clinch promotion.
Two years later, he took them to the final of the Libertadores Cup, the South American equivalent of the Champions League.
He then joined Corinthians, another hugely popular team, and led them out of the second division in 2008.
Since then, his side have won the Copa Brasil and signed former Brazil World Cup winners Ronaldo and Roberto Carlos.
CBF president Ricardo Teixeira said in a statement that the team would depend less on foreign-based players, a risky strategy which has not succeeded when it has been tried in the past.
"Brazil, as the new coach told me, will have a significant presence of players who play for Brazilian clubs, Mano Menezes is the right person to lead this process," said Teixeira.
"I am a certain he will do a great job until 2014. He showed courage and pride in having the opportunity which every coach in the world dreams of."
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