Live updates: follow the latest news on Russia-Ukraine
In a video message posted online, Mr Johnson described the atrocities committed by Russian troops as a “stain” on the country’s honour.
He urged Russians to get around Mr Putin’s controls on the media by seeking out the truth of what was happening from independent news outlets.
The Kremlin earlier claimed images of civilians said to have been killed by Russian soldiers in the town of Bucha were “fake news”, staged by the Ukrainians.
Mr Johnson said the reports were so shocking that Mr Putin had deliberately sought to hide the truth from his people.
“Your president knows that if you could see what was happening, you would not support his war,” he said.
“He knows that these crimes betray the trust of every Russian mother who proudly waves goodbye to her son as he heads off to join the military.
“And he knows they are a stain on the honour of Russia itself. A stain that will only grow larger and more indelible every day this war continues.”
Mr Johnson said people needed only a VPN connection to access independent information from around the world.
“When you find the truth, share it,” he said. “Those responsible will be held to account. And history will remember who looked the other way.”
“Your president stands accused of committing war crimes. But I cannot believe he’s acting in your name,” Mr Johnson said in Russian.