It will be the first time a British minister has been to Moscow for an official visit in more than five years and could signal a potential thaw in Anglo-Russian relations after years of antagonism.
A Foreign Office spokeswoman stressed that the visit was not a return to "business as usual", saying Britain's approach to Russia was "engage, but beware".
Relations with Russia soured after Britain sought to prosecute suspects in the killing of Kremlin critic and former spy Alexander Litvinenko, murdered by radiation poisoning in London in 2006.
Johnson was invited by his Russian counterpart Sergei Lavrov, and more detailed timings will be announced later.
"Our policy towards Russia is to 'engage but beware' and the visit is entirely consistent with this approach," the spokeswoman 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."
Johnson and Lavrov held their first telephone talks in August the same year.
Johnson has described Putin as a "ruthless and manipulative tyrant", and compared his looks to the Harry Potter character Dobby the House Elf. Yet he has called for greater cooperation with the Russian leader in the battle against the Islamic State jihadist group in Syria.
Johnson has recently hinted at a shift in Syria policy, saying President Bashar al-Assad could be allowed to run for re-election and mentioning a possible "arrangement" with regime ally Russia.
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