The former prime minister was speaking at a breakfast event at the World Economic Forum in Davos, Switzerland, where he was introduced as a “legendary figure” in Ukraine.
Asked what he thought was going through Mr Putin’s mind, Mr Johnson warned against spending too much time obsessing about the Russian leader or worrying about the escalation of the conflict.
Mr Johnson said: “Putin wants to present it as a nuclear stand-off between Nato and Russia. Nonsense. He’s not going to use nuclear weapons, OK. He’s like the fat boy in Dickens, he wants to make our flesh creep. He wants us to think about it. He’s never going to do it.”
The ex-prime minister is known to pepper his speech with literary references – in this case citing a servant character in Charles Dickens’ novel, The Pickwick Papers, known as the fat boy, who tells an old lady “I wants to make your flesh creep”.
Mr Johnson argued deploying nuclear weapons would put the Russian president into “a complete economic cryogenic paralysis”, turn states such as China and India against him, and “terrify the Russians”.
“He’s not going to do it – don’t go down that rabbit hole, stop it,” Mr Johnson added.
The former PM also urged the audience to “stop worrying about Kremlinology”, quipping: “It’s difficult to work out what’s gonna happen in UK politics, let alone in the Kremlin.”
He continued: “What we’ve got to focus on is supporting Ukraine and giving [president] Volodymyr Zelensky the tools he needs to finish the job. And they can win and they will win … give them the tanks.”
Mr Johnson was joined on the discussion panel by speakers including Dutch prime minister Mark Rutte; Yulia Svyrydenko, first vice-prime minister of Ukraine, US climate envoy John Kerry and Canada’s deputy prime minister Chrystia Freeland.
Ms Freeland used an ice hockey analogy to call for more Western support for Ukraine, saying: “I don’t skate to where the puck is. I skate to where the puck is going. This puck is going to Ukrainian victory, so let’s skate there.”
Mr Johnson chimed in “tell Putin to get the puck out of Ukraine”, prompting laughter from the audience.
Mr Zelensky reiterated his call for countries to move faster in supplying weapons as he addressed the event by video link. “The vaccine against Russian tyranny is available,” he said.
Mr Zelensky has said there are "no accidents at war time" after 14 people died in a helicopter crash in Ukraine’s capital Kyiv.
Ukraine has not claimed Russian involvement, but Mr Zelensky told the World Economic Forum the tragedy was a consequence of the war. Interior minister Denys Monastyrsky died, alongside several colleagues.
The UK has announced plans to supply Kyiv with British Army Challenger 2 main battle tanks. Prime Minister Rishi Sunak and Chancellor Jeremy Hunt are steering clear of the annual gathering of international movers and shakers in the exclusive Swiss ski resort, although the Government is being represented by business secretary Grant Shapps and international trade secretary Kemi Badenoch.