No further details of the British victim were given.
The attack is believed to have been carried out by a 42-year-old Texas resident and US Army veteran named Shamsud-Din Jabbar.
After driving the truck through the crowds the suspect is said to have got out and fired a weapon before being shot dead by police.
The FBI says an Islamic State group flag was found inside the vehicle.
Two improvised explosive devices were also found nearby, according to police.
The suspect is believed to have acted alone in a “premeditated and evil act”, the FBI has said.
At least 39 other people were injured during the attack, which took place in the city’s French Quarter – a bustling nightspot popular with locals and tourists – at around 03:15 (09:15 GMT) on Wednesday.
Some of the injured have been discharged from hospital but more than a dozen remain, with some being treated in the ICU.
Bourbon Street was opened to the public on Thursday morning ahead of the Sugar Bowl, a much-anticipated college American football match between Notre Dame and the University of Georgia, that draws thousands of attendees.
