Mutharika, the brother of the late president Bingu wa Mutharika who died in office in 2012, appealed earlier to the other 11 presidential candidates to "join me in rebuilding the country" as he took the oath of office with Vice President Saulos Chilima.
"The United States congratulates Professor Arthur Peter Mutharika and Mr Saulos Chilima on being elected the new president and vice president, respectively, of the Republic of Malawi," State Department spokeswoman Jen Psaki.
"We further congratulate the people of Malawi for actively and peacefully exercising their democratic rights in selecting their new leader."
The 74-year-old law professor takes the leadership of Malawi facing treason charges for attempting to conceal his brother's death in office two years ago, in an alleged bid to prevent Banda - then vice-president - from assuming power.
As a former foreign minister and his brother's right-hand man, he was also a leading member of an administration widely blamed for bringing the small southern African country's economy to its knees through years of mismanagement.