
"It is a wonderful opportunity, you can't turn this kind of offer down," said Sundhage in a statement.
"Brazil is a fantastic football country, rich in players and talent."
The 59-year-old Swede, who guided the USA to Olympic gold in 2008 and 2012, has been working with the Swedish federation since the London Olympics, guiding them to silver at Rio in 2016.
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Since the start of 2018, she has been in charge of the women's Under-17 national team.
Sundhage replaces Vadao whose tenure was ended on Monday after a disappointing World Cup campaign in France.
His appointment at the expense of Emily Lima, the first woman to take the role, had upset several players. Brazil struggled in the group stage and then lost to the hosts in the last 16.
Sundhage's first task will be to prepare the Brazilians for next year's Olympics in Tokyo.
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