Roch Marc Christian Kabore won elections last month, the first since long-serving ruler Blaise Compaore was ousted in a popular uprising last year.
Mr Kabore was an ally of Mr Compaore before the two fell out.
About 20 soldiers were detained on Monday for plotting to free the jailed leader of September’s short-lived coup, Gen Gilbert Diendere, officials said.
Several African heads of state attended Mr Kabore’s inauguration in the capital, Ouagadougou.
Mr Kabore said he would defend the constitution and “ensure justice for all”.
He once served as Mr Compoare’s prime minister, but gained popularity after opposing his bid to change the constitution and run for a third term.
Mr Compaore fled to Ivory Coast after being forced out of office.
Gen Diendere, a powerful ally of the ousted president, staged a coup in September.
He was forced to return power to a transitional government seven days later, after the army sided with protesters opposed to the coup.
Gen Diendere was charged in October with 11 crimes, including threatening state security. He denies the charges.
The 20 soldiers accused of trying to free him were arrested during a raid in Ouagadougou, outgoing Prime Minister Isaac Zida said.
The group had also planned to free other coup plotters, and re-establish the elite presidential guard which organised the short-lived coup, he added.
At least 57 people, including about 20 presidential guard officers, are being held over the coup.
Both Gen Diendere and Mr Compaore have also been charged with the 1987 murder of former President Thomas Sankara.
They have denied any wrongdoing.