According to the FBI, 42-year-old Shamsud-Din Jabbar, a US army veteran from Texas, was operating a pickup truck flying the Islamic State group's flag when it swerved around a police barrier and collided with New Year's Eve revelers.
According to the FBI, the motorist who was shot dead by police is not believed to have acted alone.
According to US President Joe Biden, the assailant had previously uploaded a video demonstrating his inspiration from the so-called Islamic State group.
Condemnation came later on Wednesday from countries including Britain, France, Germany and Mexico.
Sir Keir said: “The shockingly violent attack in New Orleans is horrific. My thoughts are with the victims, their families, the emergency responders and the people of the United States at this tragic time.”
Foreign Secretary David Lammy said consular officials in the US were on hand to help any British nationals affected.
“Our hearts go out to the people of New Orleans and to all those affected by this horrific attack,” he said.
“The FBI are now investigating this as a terrorist incident – this is a fast-moving situation, and we continue to wait on further information.”
German Chancellor Olaf Scholz described the attack as “senseless hatred” while French President Emmanuel Macron said: “New Orleans, so dear to the hearts of the French, has been struck by terrorism.”
Nato secretary general Mark Rutte said he was “deeply saddened” by the “horrific attack” and Mexico’s president Claudia Sheinbaum said the country stood “in solidarity with the families of the victims and with the people of the United States”.
British tourist Steve Hyde, 44, said he was in a bar in the early hours of New Year’s Day to celebrate his birthday; right by the intersection of Canal and Bourbon Street where the car careered into crowds.
He told the BBC: “We heard shots and saw people running past the window and didn’t really know what was going on… and then the sirens started.
In the hours that followed, a “heartbroken” Mr Hyde described the city’s New Year’s festivities that night as similar to “what it is like for Mardi Gras”; a “massive party” made up of “crazy numbers of people”.
In the hours that followed, he instead described a city reeling in shock.
“It’s a bit chaotic (here)… but also at the same time it’s eerily quiet,” he said.
Local authorities now believe that Jabbar, who died at the scene, may not have been alone in orchestrating the early morning assault.
Louisiana attorney general Liz Murrill told NBC News that she can say “with some certainty that there are multiple people who are involved”.
As per CNN, Ms Murrill also told the press that the collection of improvised explosive devices, which were discovered shortly after the Bourbon Street attacker was apprehended, appear to have been made in a New Orleans home.
A house fire occurred on Wednesday morning “that was connected to this event where we believe the IEDs were being made,” Ms Murrill said.
The premises, a short-term Airbnb rental, was likely leased by those involved.
Authorities overnight had already confirmed that it is suspected the New Orleans attacker may not be “solely responsible” for the attack, according to CNN.