The Foreign Secretary will demand Putin ceases its “attempt to destabilise European states” during a diplomatic state visit to Russia.
Mr Johnson is the first British Foreign Secretary to visit Moscow in five years and will hold brusque talks with his Russian counterpart, Sergei Lavrov.
He said: “Our relations with Russia cannot be ‘business as usual’ whilst Russia continues to attempt to destabilise European states, including Ukraine.”
When asked if the UK is ready to hit back at Russia, Mr Johnson said: “You can take it that in the last 18 months or so, we have certainly taken on that argument.
“The UK is certainly prepared to respond should we so desire. But I don’t want to get into what we are doing at the moment.
“I can assure you that the UK is a world leader in this field.
“We do not conduct malign or disruptive cyber activity but the logic of deterrence is clearly something we now appreciate in the cyber field.”
His comments come after it emerged that the UK is capable of crippling hostile states with cutting-edge cyber warfare.
The National Offensive Cyber Programme has boosted the UK’s electronic arsenal “substantially”, according to a report published on Wednesday by MPs on the Intelligence and Security Committee.
Speaking to The Sun, Mr Johnson added: “We have a relationship with Russia that spans over 450 years. Our similarities and historical links far outweigh our current political disagreements.
“The Kremlin has positioned Russia in direct opposition to the West, but it doesn’t have to be that way.”
A senior Foreign Office source said: “It is very important Russia understands the nature of our concern. If it does not stop what it is doing, it will see a very determined response from the West”.
The Kremlin has called Mr Johnson’s trip a propaganda coup, but the Foreign Secretary insists he is right to make it.
Mr Johnson added: “The UK and Russia are permanent members of the UN Security Council, and it’s right that we continue to talk to each other”.
Mr Lavrov invited Mr Johnson in April initially, but the trip was cancelled after Russia was suspected of being responsible for a chemical weapons attack on a rebel-held town in northern Syria, however, this claim has not been proven.
Russia has been accused of cyber attacks which include the US’ Central Command HQ, a French TV station and British MPs, but again the claims are not proven.
Mrs May attacked Russia for “weaponising information” as she announced a UK-Poland defence treaty.
She said: “The Kremlin is seeking to undermine the international rules-based system, and it will not succeed.”
The tension between Russia and the West has been dubbed the “New Cold War”.