Andrew Leak, 66, from High Wycombe in Buckinghamshire, is believed to have killed himself 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 evidence has been recovered that indicates the attack "was motivated by a terrorist ideology".
"A number of significant witnesses have been spoken to during the course of the investigation and a number of items of interest have been recovered, including digital media devices," a statement said. "Evidence from examining these items suggests there was an extreme right wing motivation behind the attack."
Police said there is no evidence Leak was working with anyone else or there is any wider threat to the public.
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 mind-set.
"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."
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 morning. 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.