Banda, a 61-year-old policeman's daughter who has won international recognition for championing the education of underprivileged girls, had served as vice president under Bingu wa Mutharika, who died on Thursday following a heart attack.
She succeeded him under the terms of the constitution.
Banda took the oath of office on Saturday in the Chinese-built National Assembly in the capital Lilongwe, as flags flew at half mast in mourning for Mutharika, whose death was only officially announced by Malawi's government on Saturday.
The two-day delay in the official announcement of Mutharika's death had raised worries that there could be a power struggle.
But fears of a political crisis in the landlocked former British colony receded as top officials and the army backed the handover of the presidency to Banda under the constitution.
Malawians, many of whom had viewed Mutharika as a stubborn autocrat, appeared to welcome their first female president.
Banda is expected to run the country until elections scheduled for 2014.
