Andrew Leak, 66, from High Wycombe in Buckinghamshire, is believed to have killed himself at a nearby petrol station after throwing two or three "crude" incendiary devices at the Western Jet Foil site, in Kent, last Sunday.
Counter Terrorism Policing South East (CTPSE) said on Saturday the attack is believed to have been "motivated by a terrorist ideology".
Evidence from digital media devices recovered during the investigation is said to suggest "an extreme right wing motivation behind the attack," police said.
Tim Jacques, senior national coordinator for Counter Terrorism Policing, said: "This was clearly a very worrying incident and although nobody was seriously hurt, two people did sustain minor injuries.
"Increasingly in counter terrorism casework, across all ideologies, we are seeing individuals who have mental health concerns and a hateful mindset.
"Assessing when this crosses the terrorism threshold is a complex process and needs to be carefully considered on a case-by-case basis.
"These decisions need to be determined by the facts, as far as they can be established at any given time.
"After considering the evidence collected so far in this case, whilst there are strong indications that mental health was likely a factor, I am satisfied that the suspect's actions were primarily driven by an extremist ideology.
"This meets the threshold for a terrorist incident."
Leak was not known to counter-terrorism police prior to the incident, CPTSE confirmed. It is understood he was also not known to the security services.
Police said there is no evidence to suggest Leak was working with anyone else or taht there is any wider threat to the public.
Facebook posts on a now-deleted account under the name of an Andy Leak from High Wycombe contain anti-Muslim sentiments and complaints about people claiming benefits if they do not speak English.
One, shared on August 9, said: "The next time the job centre sanctions your money for not looking for enough work ask them about the thousands of people getting benefits cannot speak English and can not write English, how are they looking for work?
"Unemployment benefits clearly state you cannot claim benefits if not looking for work, all of these people should be excluded from benefits.
"You can clearly not look for work if you cannot read English or speak English, they are breaking the law, time to stand up."Two members of staff at the centre were left with minor injuries after police were called at 11.22am on Sunday.
Following the incident, 700 people were moved to Manston asylum processing centre near Ramsgate for safety reasons.
Police said the investigation is ongoing, including work being carried out on behalf of His Majesty's Coroner.
An inquest into Leak's death is expected to be opened at Maidstone's County Hall on Tuesday