Mark Meechan, of Coatbridge, Lanarkshire, will be sentenced in April after a Scottish court found him guilty of communicating a "grossly offensive" video.
The 30-year-old taught his girlfriend's pug to react to the words "gas the Jews", which he repeated 23 times in the short video that he uploaded to his YouTube channel last year.
The pug was also seen raising its paw to the phrase "Sieg Heil" during the footage titled "M8 Yur Dug's a Nazi".
The video was watched more than 3 million times on the video sharing platform. Meechan was arrested after sharing the footage in April 2016.
Meechan told Airdrie Sheriff Court that he made the video to annoy his girlfriend Suzanne Kelly, 29, and denied any wrongdoing.
He said he had lost eight jobs since posting the video, adding that he only intended it to be seen by seven of his friends, who follow his YouTube channel, Count Dankula.
But he said the video was shared by someone on the social media platform Reddit, which led to the surge in its popularity.
Meechan said it was "extraordinary bad luck" the video became so popular.
Claiming the video was "for the purposes of comedy", he previously said that he had received support for the joke from famous Jewish comedian David Baddiel.
But Sheriff Derek O'Carroll said the video was "threatening and grossly offensive."
He found Meechan guilty of sending by "means of a public electronic communications network a message or other matter that is grossly offensive or of an indecent, obscene or menacing character".
Giving his verdict, Sheriff O'Carroll said: "In my view, there is no doubt it's grossly offensive."
He said Meechan knew the video was offensive as he said himself during his evidence that he "likes offensive comedy."
Update: An earlier version of this story stated than Meechan had been convicted of a hate crime. The article has been updated to reflect his conviction for 'gross offence' under the Communications Act 2003.
Sheriff O'Carroll said: "He said he chose 'gas the jews' as it was the most offensive phrase associated with the Nazi's that he could think of. It was the centrepiece of the joke. He said it was so extreme that it added to the comedy."
Meechan "knew what he was doing" he said, adding: "It is self-evident that the material is antisemitic."
He did not believe Meechan's defence that the video was made as a private joke to annoy his girlfriend and he pointed out that he had "not taken any steps to prevent the video being shared publicly".
Ephraim Borowski, 66, director of the Scottish Council of Jewish Communities (SCoJeC), told Airdrie Sheriff Court the Holocaust should not be joked about and doing so normalised antisemitism.
Mr Borowski told the court how he lost members of his own family to the Holocaust, in which over six million Jews were murdered by the Nazis.
He was shown the recording of the video in court and said: "It is grossly offensive, it stuns me that anyone should think it is a joke. My immediate reaction is that there is a clear distinction to be made between an off-hand remark and the amount of effort that is required to train a dog like that, I actually feel sorry for the dog.
"In many ways, the bit I found most offensive was the repetition of 'gas the Jews' rather than the dog itself."
In closing statements, Meechan's defence lawyer Ross Brown said: "The purpose of the video was to annoy his girlfriend. There was no evidence to demonstrate that he intended, by communicating the material, to cause fear or alarm."
He added that Meechan had only intended for the eight subscribers to his YouTube channel - all of which are friends who "share his sense of humour" - to see the video.
But Mr Brown said: "One of those friends leaked the material and so the content went viral. It was not a matter that was able to be reasonably foreseen."
He added that there was no evidence Meechan had intended to "stir up hatred on religious grounds."
He also pointed out that in a second video filmed by Meechan after the "M8" video, he had stated he had "no ill will towards the Jewish community."
He stated the video was to be seen as "comedic or satirical."
Mr Brown accused the crown of "promoting the phrase 'gas the Jews' out of the context it was intended".
He added: "Context is everything."
Mr Brown said there was no evidence of a complainer in the case, adding Police Scotland was not contacted by anyone who found the video "grossly offensive or menacing."
He slammed the authority saying Meechan's arrest was "an attempt to demonstrate diversity credentials."
He said: "The complainer would appear to be Police Scotland."