The Prime Minister said the UK would fund “cultural protection measures” in Ukraine as well as continuing to donate civil and military aid.
He also praised Eurovision winners Kalush Orchestra and said he was proud the UK would be holding Eurovision next year on Ukraine’s behalf.
Mr Johnson made the comments in a video message to the Edinburgh International Culture Summit, which is being hosted at the Scottish Parliament.
The summit brings together culture ministry delegations from around the world and has a particular focus on Ukraine this year.
"It's great to know that you're all once again committed to gather en mass for this fantastic fixture in the cultural calendar."
Prime minster @BorisJohnson appears at #EdCultureSummit via video link ▶️ pic.twitter.com/d9oTFyunWr
— Culture Summit (@CultureSummit) August 26, 2022
Mr Johnson said: “Throughout history, we’ve seen what happens when aggressors try to oppress and to eliminate culture.
“We saw it with the Nazis in the Second World War, the Khmer Rouge in Cambodia, the Taliban in Afghanistan.
“Today, the world is once again witnessing unforgivable acts of cultural vandalism, this time in Ukraine.”
He continued: “Much of Putin’s twisted rationale for his invasion rests on the vile assertion that Ukraine is somehow not a real country.
“This is a lie that he seeks to make true by systematically erasing all traces of the centuries-old Ukrainian culture from the territory his troops occupy.”
The UK will fund “cultural heritage protection measures” as well as military and humanitarian aid, he said.
The Prime Minister added: “I’m also proud, by the way, that the UK will be providing a venue in which Ukraine can host next year’s Eurovision Song Contest.
“If ever you wanted an inspirational case study on the power of culture to bring people together, then Kalush Orchestra surely provides it.”
A number of cultural figures from Ukraine are appearing at the summit, including author Oksana Zabuzhko and musician Maryna Krut.
To mark the beginning of the summit, a ceramic cockerel-shaped jug which was handed to Mr Johnson in Kyiv is going on display at Holyrood.
The Prime Minister and Volodymyr Zelensky were handed matching jugs by a woman from Kharkiv while walking through the streets of the Ukrainian capital in April.
In Ukrainian folklore, cockerels are believed to have powers of protection.
This type of jug became emblematic of Ukraine’s strong resistance against invading Russian forces after photographer Elizaveta Servatynska captured an image of a similar jug sitting undamaged on a kitchen cabinet in a high-rise apartment block in March.
The building, in Borodyanka, had been torn apart by Russian bombing.