The ceremony at a stadium in the commercial capital Blantyre was boycotted by outgoing president Joyce Banda, who was soundly beaten by Mutharika in disputed elections held on May 20.
Mutharika, who takes power in one of the world's poorest countries where 40 percent of the budget comes from aid, said the donor nations were "welcome to stay here".
Foreign policy would be based on what is best for Malawi, he said.
Mutharika said he regretted Banda's absence, saying she had "declined to come here and hand over power to me.
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"I was looking forward to shaking her hand and burying the past. I have an olive branch in my hands."
A spokesman for Banda said: "She was not officially invited and her official presidential convoy was withdrawn early hours of Saturday as soon as it was announced that Peter Mutharika had won the presidency.
"It would have been difficult for the outgoing president to travel to Blantyre."