He pledged to uphold the “integrity (and) unity” of the West African nation in a ceremony overseen by parliament speaker Cavaye Yeguie Djibril.
Biya, who has ruled the country for 35 years, was declared victor in the October 7 vote with 71 percent of the ballot.
But the elections were marked by low voter turnout, violence and allegations of fraud.
On the eve of Biya’s inauguration, 79 students and three supervisors, including their headmaster, were abducted from a school in the Northwest Region, where anglophone separatists have launched an armed campaign for independence.
Cameroon’s 22 million people are mainly French-speakers, but around a fifth are English-speaking.
In 2016, resentment at perceived discrimination in education, the judiciary and the economy fanned demands for autonomy in the Northwest and neighbouring Southwest Region.
In 2017, as Biya refused any concessions, radicals declared an independent state — the “Republic of Ambazonia” — and took up arms.
Attacks by the secessionists and a crackdown by the authorities have led to the death of at least 400 civilians this year as well as more than 175 members of the security forces, according to an NGO toll.
More than 300,000 people have fled the violence, many of them living hand-to-mouth in the forests, and some across the border into Nigeria.
In the October election, turnout was a meagre five percent in the Northwest and 15 percent in the Southwest — but Biya won more than two-thirds of the vote in both regions.