Johnson has been a vocal critic of Russia's foreign policy in the past, particularly regarding its military interventions in Syria and Ukraine.
The Foreign Office said in a statement that the visit, at Russia's invitation, had "been in the pipeline for some time" following discussions between UK Prime Minister Theresa May and Russian President Vladimir Putin in September.
"The Prime Minister and the Foreign Secretary have made clear that our policy towards Russia is to 'engage but beware' and the visit is entirely consistent with this approach," the statement said.
"Discussions will focus on the UK-Russia relationship and current international issues including Syria and Ukraine, where we continue to have significant differences. This is not a return to business as usual and the Foreign Secretary will continue to be robust on those issues where we differ."
It added, "We have always been clear that the UK will engage with Russia where it is in our national interest to do so."
The exact timing of the trip has not been confirmed yet.
Johnson: 'Complicity in war crimes'
Johnson, who was appointed the top UK diplomat in July, has been outspoken in his criticisms of Russia's support for Syrian President Bashar al-Assad.
In a speech at the Conservative Party Conference in October, Johnson spoke of "the continuing savagery of the Assad regime against the people of Aleppo and the complicity of the Russians in committing what are patently war crimes
," a reference to Moscow's role in the battle to retake the key Syrian city
The Syrian regime has claimed it has been fighting "terrorists" -- its term for rebel fighters.
A couple of weeks later, speaking alongside then-US Secretary of State John Kerry, Johnson appealed for Russia to "do the right thing by humanity" and seek a ceasefire in Syria.
In January, Johnson signaled a shift in tone while addressing a committee in the House of Lords, when he noted Moscow's role in bringing about Syrian peace talks in Astana, Kazakhstan, following its military involvement in Syria.
"To the extent that the Russians are capable of getting a ceasefire and stopping suffering, that must be rated a plus," Johnson said. "That comes, of course, after a pretty brutal and barbaric bombardment of Aleppo and other places which they facilitated -- or, I'm sure, perhaps even participated in."
He also described Russia's involvement in Syria as a "fact of life" after other powers, such as Britain, had declined to step in.
However, Johnson this week said he was "deeply disappointed" that Russia, along with China, had blocked the UN Security Council from taking action over chemical weapons use in Syria.
He also voiced Britain's "unwavering support" for Ukraine on a visit to Kiev this week, adding that the UK government is "adamant that Russia's annexation of Crimea is illegal and we urge Russia to return it
Russia annexed Ukraine's Crimea territory in 2014 and is accused of involvement in the conflict in eastern Ukraine
between pro-Russia separatists and the Ukrainian armed forces.
European unease, US questions
Johnson's planned visit to Moscow will take place against a backdrop of unease in Europe over what is perceived as increased Russian aggression, and questions in the United States over alleged ties between US President Donald Trump's campaign and Russia
NATO has stepped up its efforts to support Eastern European allies from potential aggression by Russia in recent months, with multinational exercises and the buildup of US troops in Europe.
Sweden this week announced it was reintroducing compulsory military service
"as a response to the new security situation" in Europe.