Benjamin Hannam, 22, of Edmonton, north London, was also convicted of lying on his application and vetting forms to join the Met and having terror documents detailing knife combat and making explosive devices.
On his application form he denied ever being a “member of the BNP or similar organisation”.
A jury had deliberated for more than 32 hours to find Hannam guilty on Thursday.
Judge Anthony Leonard QC lifted a ban on reporting the case after Hannam admitted possessing an indecent image of a child, which was to have been the subject of a separate trial.
Hannam, who is suspended from duty, had been working as a probationary officer for the Met for nearly two years before he was found on a leaked database of users of extreme right-wing forum Iron March.
He had signed up to the forum when he joined the London branch of neo-Nazi group NA in March 2016.
The officer, who has autism, said he was “desperate to impress” an older NA organiser who gave him free stickers and badges.
Hannam’s association with NA ended before he began working for the Met and counter-terrorism officers acted “swiftly” once he had been identified as a suspect.
Commander Richard Smith, head of the Met’s counter-terrorism command, said it was a “unique” case.
He said: “Ben Hannam obviously lied on his application form to join the Met.
“He would never have been able to join had we known then of his interest in the extreme right wing and his previous membership of National Action.
“Once we identified his involvement with that organisation we took immediate steps to arrest him and put him before the court.”
He stressed there was no evidence Hannam abused his position “to further his extremist views”.
The extreme right-wing group NA, labelled “racist, anti-Semitic and homophobic” by the then home secretary Amber Rudd, was banned in December 2016 after a series of rallies and incidents, including praise of the murder of MP Jo Cox.
Founded in late 2013 by university students Alex Davies and Benjamin Raymond, it was based on neo-Nazi ideology and hatred of members of Jewish, gay and ethnic minority communities.
It targeted Britain’s disaffected male youth through slick online propaganda and drew heavily on the virulently racist rhetoric and symbols of Adolf Hitler’s Nazi party.
Stunts by activists included the desecration of the statue of Nelson Mandela in Parliament Square, placing a banana in his hand.
Propaganda videos of demonstrations across England and Scotland showed men in skull masks waving banners and making Nazi salutes.
In his first post on Iron March, Hannam wrote that he was “completely swayed” by NA.
He went on to try to recruit a new member via Iron March saying it is “always good for more people to join, means we can arrange more stuff which is just more fun for everybody!”
He told him that most NA guys agreed the “Hitler was right” slogan was “a bit too edgy” but added: “Then again it is pretty funny and we all know our stance on the big man.”
At the NA national conference in Liverpool in April 2016, Hannam posed in an official photograph on Crosby Beach.
Hannam continued to meet high-profile people linked to the group in early 2017, after it was banned, and in July he spray painted the symbol for an NA alias – NS131 – in a storm drain on the outskirts of Swindon, which was filmed for a promotional video.
Days later Hannam applied to join Scotland Yard, fraudulently denying he had ever been a member of the British National Party “or similar organisation”.
When officers searched his bedroom last year, they found neo-Nazi posters, notes detailing his membership of NA, as well as NA badges and business cards.
As early as May 2014, Hannam had expressed intolerant views, writing: “I’m not racist, I just don’t like people who’s skin is darker than mine! (sic)”
He had stored on a USB stick two documents said to be useful to a terrorist.
They were mass murderer Anders Breivik’s manifesto, which contained guidance on making radiological, chemical and biological weapons and improvised explosive devices, and a second document detailing how to carry out a fatal knife attack.
In his defence, Hannam denied he had ever been a member of NA before or after it was banned.
He told jurors he had been attracted to fascism aged 16 because of its bold artwork and contacted NA after seeing propaganda online.
Hannam told jurors: “I was under the impression this was some kind of youth network.
“I have never been stickering with NA nor have I done banner drops. I stuck to social activities.
“Most of the time was going to the pub and going for walks. Other times camping or going boxing.”
He denied reading all of Breivik’s manifesto, saying he found it “boring”.
Another NA member, Jack Renshaw, was jailed for life in 2019 for plotting to kill a Labour MP two years earlier.
After he was found guilty it was revealed he was also a convicted paedophile who had been jailed for 16 months in 2018 for grooming two underage boys online.
Other convicted National Action members include Adam Thomas, 22, and Claudia Patatas, 38, a “fanatical” neo-Nazi couple who named their baby son after Hitler.
Additional reporting by PA.