She becomes Southern Africa’s first female head of state after taking the oath before parliament in the Malawian Capital, Lilongwe.
Mrs Banda, has been vice president since 2009.
Meanwhile, Malawian Ambassador to Zimbabwe, Professor Richard Phoya has paid tribute to Malawians for remaining calm and united, honouring the constitution at a time when every Malawian both at home and outside is still trying to come to terms with the death of President Wa Mutharika.
In an interview with ZBC News at his Mandara residence in Harare, Ambassador Phoya said President Wa Mutharikaâ€™s body is still in South Africa, while his government is finalising the burial itinerary.
Professor Phoya commended Malawians for remaining calm and accepting the swearing in of Ms Banda as the new head of state as stipulated in the countryâ€™s constitution.
He said speculation was already mounting that Malawi could face a succession crisis since Mrs Banda had been fired from the ruling Democratic Progressive Party (DPP) and had formed the Peopleâ€™s Party.
Ambassador Phoya said a book of condolences will be opened from Tuesday the 10th to Friday the 13th at the Malawian Embassy at number 9/11 Duthie Road, Alexandra Park, Harare.
The late Wa Mutharika, who suffered a heart attack on Thursday, was elected President of Malawi in 2004 and won a second term in 2009.
After collapsing on Thursday morning, President Wa Mutharika was rushed to Kamuzu Central Hospital in Lilongwe before being airlifted to South Africa, where he was pronounced dead.
Malawi has since declared 10 days of mourning.
Burial arrangements will be announced in due course.