Chakwera, 65, a former evangelist preacher, was declared the victor with almost 59 per cent of the vote, according to results announced on Saturday.
"I do solemnly swear that I will well and truly perform the functions of the high office of the president of the Republic of Malawi and that I will preserve and defend the constitution," said Chakwera said as he took his oath before thousands of supporters.
Saulos Chilima was sworn in as vice-president.
Nearly 7 million Malawians returned to the polls on Tuesday after the country's supreme court found the first election had been marred by widespread irregularities - including the use of correction fluid to tamper with result sheets.
Winner
Chakwera, the leader of the Malawi Congress party, was pronounced the winner with 2.6 million votes, while President Peter Mutharika took 1.75 million. Peter Dominico Kuwani claimed just over 32,000 votes
Mutharika, whose Democratic Progressive party had held power since 2014, had won 38 per cent of the discredited vote last year, just ahead of Chakwera with about 35 percent.
Malawi is only the second African country south of the Sahara to have presidential poll results overturned in court, after Kenya in 2017. And it is the first time in the region that a vote re-run has led to the defeat of an incumbent leader.
"Fellow Malawians, to stand before you is an honour. It's an honour that fills me with unspeakable joy," Chakwera said.
"It is an honour forged in the furnace of your desire and your demand for change."
Addressing supporters in Lilongwe's Freedom Square, Chakwera vowed to offer a government that served all the people.
Service
"There are many of you who did not vote for me in this election,” he added. “And perhaps the prospect of my presidency fills you with fear, "But Malawi is home to you too ... so long as I am its president, you too will prosper."
Mutharika, 79, had argued that the election re-run had been flawed, citing violence and intimidation against monitors.
But the Malawi Electoral Commission dismissed the claims and his request to annul the results of the second vote and declare a third poll.
