Police shot the driver dead after he barrelled the truck two kilometres (1.3 miles) through a crowd that had been enjoying a fireworks display for France's national day.
The palm-lined Promenade des Anglais of the French Riviera resort was left strewn with bodies as hundreds fled in terror.
Authorities said they found identity papers belonging to a 31-year-old French-Tunisian citizen in the 19-tonne truck, and that the driver had fired a gun several times before police shot him dead.
He has been named by local media as Mohamed Lahouaiej Bouhlel.
The attack was of an “undeniable terrorist nature,” a sombre Hollande said in a televised national address, confirming that several children were among the dead.
“France was struck on its national day … the symbol of freedom,” said Hollande.
Interior ministry spokesman Pierre-Henry Brandet said 84 people were killed and scores injured, including 18 in “critical condition”.
Witnesses described the horror they saw.
“We got off our bus near the Hotel Negresco and started walking down the promenade,” Swedish holidaymaker Kristian Julius told The Local.
“For no particular reason I turned around and saw a truck that was veering backwards and forwards along the promenade. It was aiming at people. It then came directly at us, so we ran towards the street. If I hadn’t turned round when I did I would have been crushed,” Julius added.
“I knew within a couple of seconds that this was a terror attack. The truck was completely dark, there were no lights on, so you couldn’t see the driver. A man threw himself at the cab and tried to get inside, but he was thrown off.
“We saw two people who had been killed, and an old woman whose leg was torn off at the knee. It was the old people and children who couldn’t get away quickly enough who were hurt – it’s so cowardly.”
Bastille Day is a celebration of everything France holds dear — its secular republic and the values of “Liberte, Egalite, Fraternite” (Freedom, Equality, Fraternity).
Earlier Thursday, onlookers had enjoyed a day of military pomp and ceremony in Paris — where armed forces, tanks and fighter jets swooped down the Champs Elysees avenue — and spectacular firework displays.
'Holding cold hands'
In a video viewed over 3,000 times on Facebook, a trembling Tarubi Wahid Mosta recounted the horror on the promenade, where he took photos of an abandoned doll and pushchair and came home with a victim's Yorkshire terrier.
“I almost stepped on a corpse, it was horrible. It looked like a battlefield,” he said.
In a series of posts, he described the sense of helplessness faced with the carnage.
“All these bodies and their families … they spent hours on the ground holding the cold hands of bodies dismembered by the truck. You can't even speak to them or comfort them.”
As the sun rose over the picturesque bay, forensic police swarmed the resort, which has drawn sun-seekers and the jet-set since the 19th century with its pebble beaches and clear blue water.
The truck was riddled with bullet holes and badly damaged, with burst tyres.
Robert Holloway, an AFP reporter who witnessed the white truck driving at speed into the crowd, described scenes of “absolute chaos”.
“We saw people hit and bits of debris flying around. I had to protect my face from flying debris,” he said.
On Twitter, there were desperate pleas from those looking for news of loved ones. Pictures of a young girl with braces and a teenager pulling a funny face were among dozens posted.
— Le JDD (@leJDD) July 15, 2016
'Horrific terrorist attack'
The attack was the third major strike against France in less than 18 months and prosecutors said anti-terrorist investigators would handle the probe.
It comes eight months after Islamic State attacks on Paris nightspots left 130 people dead, dealing a hard blow to tourism in one of the world's top destinations.
US President Barack Obama condemned “what appears to be a horrific terrorist attack”, although no group had yet claimed responsibility.
Hollande announced he would extend France's state of emergency for three months in the wake of this latest attack and “step up” the government's action against jihadists in Syria and Iraq.
“We will continue striking those who attack us on our own soil,” he said, in reference to the Islamic State group.
He also called up army reservists to bolster security services that are stretched to the limit. France has been under a state of emergency ever since the November 13 Paris carnage, which came after 17 were killed in another attack in January at various sites including the offices of the Charlie Hebdo magazine and a Jewish supermarket.
Isis has repeatedly singled out France as a prime target for its military action against the group in Iraq and Syria, and hundreds of jihadists have left France to go and fight in its ranks.
'He crushed a lot of people'
A witness named Nader told BFM television he had seen the whole attack from start to finish, and had initially thought the driver had “lost control”.
“He stopped just in front of me after he (crushed) a lot of people. I saw a guy in the street, we were trying to speak to the driver to get him to stop.
“He looked nervous. There was a girl under the car, he smashed her. The guy next to me pulled her out,” he said in broken English.
Nader said he saw the driver pull out a gun and start shooting at police.
“They killed him and his head was out the window.”
A source close to the investigation said an “inactive” grenade was found inside the truck, as well as “several fake rifles”.
Over the past week, France had been breathing a sigh of relief after successfully hosting the month-long Euro 2016 football championship, which passed off without incident despite fears of attacks.
The tournament brought an all-too-brief burst of joy to a gloomy France, bogged down after the two attacks in 2015, violent anti-government protests, strikes and floods.