Shehroz Iqbal, 29, posted the mobile phone footage to a WhatsApp group of like-minded friends on 11 March this year with the words “Attack, attack”.
He had denied encouraging terrorism and disseminating Islamic State propaganda on Facebook but was convicted after a trial at the Old Bailey.
Iqbal, from Ilford, east London, was jailed for eight-and-a-half years.
The court heard the posts had been uncovered on his phone when he was pulled over later that month for possession of drugs.
In court, prosecutor Kate Wilkinson described Iqbal as an extremist who was “volatile and prone to act on his extremism”.
He spent an hour-and-a-half at the Hayward Gallery on the Southbank, near the Royal Festival Hall and Waterloo Bridge, making the clip which he sent to a WhatsApp group of 22 associates called From Dark To Light.
While on bail for the drugs matters and the video, Iqbal posted a 2015 propaganda video depicting Islamic State fighters on social media.
The court heard the video, which featured an image of a dead body, was viewed more than 200 times on the defendant’s Facebook page.
On his arrest in April he claimed he had been high on drugs when he posted the Facebook video without looking at it.
He also claimed he made the video at the Hayward Gallery he said he had made the film to show off his bike, but he declined to give evidence at trial.
At his sentencing hearing on Friday, the court heard Iqbal had been subject to two suspended sentences at the time of the offences for harassing members of a synagogue in Gants Hill.
He also had a string of previous convictions for shoplifting, threatening behaviour and driving offences, as well as possession of drugs stretching back to 2010.
His defence barrister Laurie-Anne Power said he had been “seeking the approval” of other people in the WhatsApp group.
“He was someone who was given very little regard – often dismissed and often ignored,” she said.
She said that prior to the offending, Iqbal had sought help from an anti-extremism programme, saying: “I am sitting online all day and watching this material, and it is consuming me.”
Ms Power said Iqbal had turned to drug dealing during the first coronavirus shutdown when he lost his job as a carpet fitter and that he was so inept he had kept voice memos of all of his conversations with his co-accused and the people he was supposed to be delivering the drugs to.
His sentence is also for supplying class A drugs and two counts of possession of drugs.
Judge Philip Katz QC said he did not believe Iqbal’s approach to an anti-radicalisation programme to be a “genuine change of attitude” and that when dealing with authorities he says “whatever you think suits you best at the time”.
He continued: “You blame your offending on everything from drugs to mental issues to your difficulties opening a bank account, and most ironically to you being the subject of racism.
“The irony being your own overt racism, some of it towards other Muslims.”