At least 80 were killed, 18 were critically injured and many others suffered injuries, according to French officials.
The attack was believed to be a deliberate act of terrorism, French officials said.
Eyewitnesses said the driver got out of the truck after driving into people on a sidewalk and began firing a gun into the crowd. Police fired back, killing the driver, officials said.
The president of the regional government, Christian Estrosi, also told French TV that the truck was driven by someone who appeared to have "completely premeditated behavior."
He added that "the truck was loaded with arms, loaded with grenades."
The truck's windshield was visibly riddled with bullet holes after the gun battle.
French President Francois Hollande said the terrorist character" of the Bastille Day truck attack in Nice could not be denied. Hollande said the victims included children.
Just hours after announcing in the traditional Bastille Day interview that the state of emergency, in place since November attacks that killed 130 in Paris, was to be removed, Hollande said it must be extended for three months.
That decision will need parliamentary approval.
The city was on lockdown amid fears of a terror attack.
Il s'agit du pire drame de l'histoire de Nice car plus de 70 victimes sont déjà à déplorer.— Christian Estrosi (@cestrosi) July 14, 2016
Eyewitnesses described an "apocalyptic" scene on one of the most famous streets in Europe.
The crowd had gathered on the Promenade-des-Anglais to watch the Bastille Day fireworks. That street was then lined with bodies.
The US Consulate in Marseille issued an emergency message to Americans in the south of France: "We are working with local authorities to determine if any U.S. citizens were injured in the event. We urge U.S. citizens in Nice to contact family members and loved ones to notify them that you are safe, avoid the area, to monitor local press for updates, and to exercise caution if you are in the vicinity."
President Barack Obama issued a statement condemning the attack and offering assistance to French officials.
"On behalf of the American people, I condemn in the strongest terms what appears to be a horrific terrorist attack in Nice, France, which killed and wounded dozens of innocent civilians," Obama said. "Our thoughts and prayers are with the families and other loved ones of those killed, and we wish a full recovery for the many wounded."
U.S. officials said Americans who were concerned about relatives or friends in Nice can reach out to the State Department online or call the Bureau of Consular Affairs in Washington at (888)407-4747 toll-free in the United States and Canada or 1-202-501-4444 from other countries from 8:00 a.m. to 8:00 p.m. Eastern Standard Time, Monday through Friday (except U.S. federal holidays).
The French government also set up a crisis line at +33-820-26-0606.
Writing online, Nice Matin journalist Damien Allemand who was at the waterside said the fireworks display had finished and the crowd had got up to leave when they heard a noise and cries.
"A fraction of a second later, an enormous white truck came along at a crazy speed, turning the wheel to mow down the maximum number of people," he said. "I saw bodies flying like bowling pins along its route. Heard noises, cries that I will never forget."
Allemand said people took shelter in a nearby restaurant, where he continued to hear people shouting for missing family members. He ventured out and saw bodies, blood and body parts all along the road.
"This evening, it was horror," Allemand concluded.
The Associated Press contributed to this report.