French president-elect Emmanuel Macron and his wife Brigitte Trogneux.
Macron is the youngest president in the country's history and the eighth president of France's Fifth Republic, created in 1958.
Macron announced his determination to push ahead with reforms to free up France's economy and pledged to press for a "more efficient, more democratic" EU.
Earlier, Mr Macron was handed France's nuclear codes, putting him in charge of what will be the EU's only arsenal of atomic weapons after Brexit is complete.
Macron has promised to refresh France's parliament and his party - La Republique En Marche (REM, Republic on the Move) - unveiled 428 out of its 577 candidates this week.
In a visibly moving moment for both, Macron accompanied Hollande to his vehicle, shaking hands and applauding him along with the employees of the French presidency who had gathered in the palace's courtyard.
The new leader also took time to pose at the front porch of the Elysee with his 64-year-old wife Brigitte Macron.
Mr Macron had been Mr Hollande's top economy adviser from 2012 to 2014, then became his economy minister until a year ago, when he chose to quit the Socialist government and launch his independent presidential bid.
Outgoing French President Francois Hollande, at left, welcomes incoming French President Emmanuel Macron as he arrives for his inauguration ceremony at the Elysee palace in Paris on Sunday.
Her three children from her previous marriage were also present along with VIPs from France's political scene and the young team of advisors behind Macron's sensational rise. Macron was Hollande's former adviser, then his economy minister from 2014 to 2016, when Macron quit the Socialist government to launch his own independent presidential bid.
Prime Minister Hailemariam Dessalegn congratulated Emmanuel Macron on being elected the 25th President of France.
"In order to be the man of one's country, one must be the man of your time", Fabius told the new president, quoting the Romantic-era French writer Chateaubriand.
Macron is seeking to kickstart the French economy and overcome the sense of political malaise gripping the country.
Numerous candidates are newcomers in politics. Unlike his opponent, Macron is a strong believer in the European Union, and he will meet German Chancellor Angela Merkel Monday to "relaunch the European project".
Macron's rise, marked by a 21-gun salute at the Esplanade des Invalides, signaled at least a pause in the anti-globalization trend that elevated businessman Donald Trump into the USA presidency and led British voters to choose Brexit.
Macron then walked alone across the cobblestones of the Champs-Elysees avenue to the Arc de Triomphe, where he lay a wreath and re-ignited the flame at the tomb of the unknown soldier. Half have never held elected office, including a retired female bullfighter and a star mathematician, and half are women.
More than 230 people have died in France in attacks claimed by Islamic State over the past two years as the country has taken part in military action against the militant group that controls parts of Syria and Iraq. "France remained France", he tweeted.