Witnesses said the driver crashed his truck into a huge gathering of people on the Promenade des Anglais, jumped out and then opened fire with a gun.
In a Tweet posted 10 minutes before uploading the short clip Mr Terry wrote: 'Seems to be under control in #nice but the mass panic was like (nothing) I'd never seen.'
UTV Ireland producer Ben Terry said: 'We were actually enjoying the fireworks display on Promenade des Anglais and we just turned off the street and two seconds later we saw people running towards us.
'We heard several gunshots, of course we had no idea where they were coming from, but after the Paris attack and we what saw in Brussels recently there was a sense of tension and we ran with the crowd.'
He added: 'We managed to run up the side ally into a restaurant and we quickly ran into a store room there and were huddled up with a bunch of other people. Several of them were crying, some were trying to call their family and more and more people were running in.
'A few of them looked to be injured, possibly just injuries they received while trying to get away from scene, but the sense of panic was everywhere.'
Gunmen are thought to have started to fire during the attack, and a spokesman for the Alpes Maritime prefecture advised locals to 'stay indoors' as the shots were heard.
The attack comes as President Francois Hollande today announced that the state of emergency which France declared after last November's deadly Paris attacks will be lifted on July 26.
