His comments come as spy chiefs warn British political party leaders about the threat of Russian hacking at the next general election.
A senior Government source has confirmed to Sky News a cyber security summit will be held to discuss fears of interference from Moscow.
Officials at GCHQ, the UK’s eavesdropping agency, fear Russian hackers could steal and leak internal emails or publish private databases of voters’ political views, according to the Sunday Times.
The National Cyber Security Centre, which is part of GCHQ, offered in the letter to party leaders to help strengthen the parties’ security systems, the newspaper said.
“You will be aware of the coverage of events in the United States, Germany and elsewhere reminding us of the potential for hostile action against the UK political system,” the letter from chief executive Ciaran Martin reportedly stated.
“This is not just about the network security of political parties’ own systems.
“Attacks against our democratic processes go beyond this and can include attacks on parliament, constituency offices, think tanks and pressure groups and individuals’ email accounts.”
Fears over potential Russian interference have heightened in recent months, amid allegations of meddling in the electoral processes of a number of countries.
In December, Germany’s domestic intelligence agency claimed Russia was trying to destabilise the country with propaganda and cyber attacks ahead of its general election later this year.
And an aide to French presidential candidate Emmanuel Macron recently told Sky News the candidate is being targeted by Moscow in a parallel campaign of hacking and fake news.
Mr Johnson, who was speaking in an interview with ITV’s Peston On Sunday, said: “Bringing down French TV stations, you’ve seen what happened in the United States where there is no question at all that they were involved in the hacking of the Democratic National Convention.
“You’ve seen what happened in Montenegro where there was an attempted coup in a European state and possibly even an attempted assassination of the leader of that state.
“There is very little doubt that the Russians are behind these things.”
Asked about claims of Russian hacking Mr Johnson said: “We have no evidence that the Russians are actually involved in trying to undermine our democratic process at the moment. We don’t actually have that evidence.
“But what we do have is plenty of evidence that the Russians are capable of doing that. And there is no doubt that they’ve been up to all sorts of dirty tricks.”
Mr Johnson is due to visit Russia and meet his Russian counterpart Sergei Lavrov later this month.