Mr Maada Bio is a former military ruler who briefly ruled the country in 1996.
He narrowly beat ruling party candidate Samura Kamara, who has alleged irregularities and says he will challenge the outcome in court.
Mr Maada Bio was sworn in on Wednesday, less than two hours after being declared the winner of Saturday’s vote.
In a televised address, Mr Kamara said: “We dispute the results and we will take legal action to correct them.” He also urged his supporters to stay calm.
Mr Maada Bio, leader of the Sierra Leone People’s Party (SLPP), won just under 52% of the vote.