Britain last year sent 100 troops to help Poland deal with a migrant crisis at its border with Belarus, Polish state news agency PAP reported.
"We will add to those ... by sending a further 350 British troops to Poland as a bilateral deployment to show that we can work together and send a strong signal that Britain and Poland stand side by side," Wallace said at a joint news conference with Błaszczak.
The UK defence ministry said in a statement that Poland and Britain "have a long history as defence partners and NATO Allies."
It added that Błaszczak and Wallace discussed "our response to the build-up of Russian forces on the border with Ukraine and the impact for European security" during their meeting in London.
Błaszczak thanked Britain for its "further support and strengthening of NATO's eastern flank," voicing his appreciation of "the presence of British troops in Poland."
He said: "We are facing another challenge in the form of a security threat. Through the policy of deterrence, we want to discourage the aggressor from taking any further action."
The UK defence ministry's press office said in a tweet 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."
According to the Polish defence ministry, Błaszczak and Wallace talked about "the Russian threat to Ukraine and Central European countries" and tensions at Poland's eastern border with Belarus.
Other topics included cybersecurity, it said.
UK Prime Minister Boris 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: IAR, BBC, Reuters