Dilma Rousseff said she had been given the most important mission of her life
The woman elected to be Brazil's first female president has promised to make gender equality a priority.
Ms Rousseff also promised to fight poverty and maintain continuity with her highly popular predecessor, Luiz Inacio Lula da Silva.
She won Sunday's presidential run-off election with 56% of the vote to rival Jose Serra's 44%.
Ms Rousseff takes office on 1 January next year when President Lula steps down after completing the constitutional limit of two consecutive terms.
Her election as the country's first female leader was a sign of the democratic progress Brazil had made, Ms Rousseff said in her victory speech in the capital, Brasilia.
"So I am here stating my first post-election commitment: to honour Brazilian women so that this fact - unprecedented until now - becomes something normal and can be repeated and expanded in companies, public institutions, and organisations that are representative of our entire society."
She continued: "I would like very much today for fathers and mothers of daughters to look in their eyes and tell them: 'Yes, a woman can.'"
Ms Rousseff, a former Marxist rebel who was imprisoned for three years in the early 1970s for resisting military rule, promised to protect freedom of expression and worship, and to honour the constitution.
End Quote Luiz Inacio Lula da Silva Brazilian president
"I reiterate my fundamental promise: the eradication of poverty," she said. "We must not rest while there are Brazilians going hungry."
Ms Rousseff, 62, has never before held elected office. She trained as an economist and worked her way up through local and state governments.
She joined President Lula's cabinet as energy minister in 2003-5 and then became his chief of staff.
She paid tribute to her predecessor and promised continuity with his left-leaning policies. She is expected to emphasise government efficiency, expand the role of the state in some sectors such as mining, and upgrade the country's decrepit infrastructure.
"The task of succeeding him is difficult and challenging. But I know I will honour this legacy and extend his work," she said.
"I will knock on his door often, and I know it will always be open."
She will also oversee a huge expansion of Brazil's oil industry, following the discovery of major offshore fields that should make Brazil one of the world's top 10 oil exporters.
She can count on strengthened majorities for the governing coalition in both houses of Congress to help ease the task of pushing her legislative agenda.
Ms Rousseff's victory owed much to the extraordinary popularity of the outgoing President Lula, who endorsed her as his successor for the governing Workers' Party from the start.
Lula, who has to step down after completing two consecutive terms - the maximum allowed, said he would not interfere in her government.
Ms Rousseff will have "to form a government in her own image - I only hope she achieves more than I did", he said after casting his vote.
He added that he would not be attending public victory celebrations because "this is her party".