Johnson is set to hold talks with Polish Prime Minister Mateusz Morawiecki and will also meet with President Andrzej Duda, according to officials.
He is scheduled to visit British soldiers stationed in the country.
Earlier in the day, Johnson headed to Brussels to meet with NATO Secretary-General Jens Stoltenberg.
Speaking at a joint news conference with Stoltenberg, Johnson said that the West's standoff with Russia over Ukraine "is the biggest security crisis that Europe has faced for decades."
He added: "And I think that the combination of sanctions and military resolve, plus diplomacy are what is in order."
Boris Johnson and Jens Stoltenberg meet in Brussels on Thursday. Photo: EPA/OLIVIER HOSLET
Amid a Russian military buildup near Ukraine, UK Defence Secretary Ben Wallace said earlier this week that Britain would send an additional 350 troops to Poland.
The UK defence ministry's press office said in a statement at the time that 350 Royal Marines would deploy to Poland to support the country "with joint exercises, contingency planning and capacity building as the build-up of Russian forces on Ukraine’s border continues."
Britain last year sent 100 troops to help Poland deal with a migrant crisis at its border with Belarus.
The Polish president on Tuesday met for talks with his French counterpart and the German chancellor in Berlin, and the three leaders said that a war in Ukraine must be averted, amid concern over the Russian military buildup.
Britain's Johnson last week expressed deep concern about Russia's hostile activity on the Ukrainian border in a call with Russian President Vladimir Putin, the BBC reported.
Johnson warned Putin that any further incursion by troops on the border would be "a tragic miscalculation" by Russia, according to the British public broadcaster.
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Source: PAP, Reuters