Ms Bachelet defeated Chile's richest man Sebastian Pinera to win a convincing victory in a run-off election in January.
She inherits a country with a booming economy but a widening gap between rich and poor.
The new president has promised to build a more equitable and tolerant society and to give a greater voice to women and indigenous people.
Guests at the inauguration included Venezuelan President Hugo Chavez, Bolivian President Evo Morales and US Secretary of State Condoleezza Rice.