The thousands of people who packed the National Congress in Brasilia included 23 heads of state, U.S. Secretary of State Hillary Clinton and 23 of her counterparts from other countries and 11 of Rousseff's former cellmates from Tiradentes Prison, CNN reported.
"From now on I am the president of all Brazilians," Rousseff said, weeping.
Rousseff was the handpicked successor of Luiz Inacio Lula da Silva after serving as his chief of staff. She won a runoff election in October.
The crowd sang the anthem of the PT Workers' Party, "Ole, ole, ole, ola, Lula, Lula."
The daughter of a Communist who fled his native Bulgaria in the 1920s and became prosperous in Brazil, Rousseff became a Marxist after a 1964 coup established a right-wing dictatorship. She was arrested in 1970 and later said she was "diabolically tortured" for months.
Rousseff and her longtime partner and former comrade Carlos Araujo became involved in elective politics in the 1980s.