The then-prime minister said Putin told him it "would only take a minute," BBC reports, referring to its documentary, examining Putin’s interactions with world leaders.
Johnson warned Putin that invading Ukraine would lead to Western sanctions and more NATO troops on Russia's borders.
He also tried to deter Russian military action by telling Putin that Ukraine would not join NATO "for the foreseeable future".
But Johnson said: "He threatened me at one point, and he said, 'Boris, I don't want to hurt you but, with a missile, it would only take a minute' or something like that. Jolly.
"But I think from the very relaxed tone that he was taking, the sort of air of detachment that he seemed to have, he was just playing along with my attempts to get him to negotiate."
President Putin had been "very familiar" during the "most extraordinary call", Johnson said.
Less than a fortnight later, as tanks rolled over the border on 24 February, Johnson received a phone call in the middle of the night from President Volodymyr Zelensky of Ukraine, the report says.
"Zelensky's very, very calm," Johnson recalled. "But, he tells me, you know, they're attacking everywhere."