In a statement, Dominic Raab said there was "undeniable evidence" that Alexei Navalny was poisoned by the military nerve agent, which was developed by Russia.
He added: "Despite having a clear case to answer, the Russian authorities continue to make no credible attempt to investigate this attack.
"There is no plausible explanation for Mr Navalny's poisoning other than Russian involvement and responsibility for this appalling attack."
Mr Raab's statement came after the Organisation for the Prohibition of Chemical Weapons confirmed findings from two laboratory tests performed after Mr Navalny fell ill.
The Russian opposition leader was taken to hospital in Germany after he was exposed to the nerve agent on 20 August.
Russia has denied accusations from Mr Navalny that the state was involved in the poisoning.
France and Germany released a joint statement saying they would propose sanctions against Russian individuals to the European Union.
They said: "No credible explanation has been provided by Russia so far. In this context, we consider that there is no other plausible explanation for Mr Navalny's poisoning than a Russian involvement and responsibility."
The joint statement added: "Drawing the necessary conclusions from these facts, France and Germany will share with European partners proposals for additional sanctions.
"Proposals will target individuals deemed responsible for this crime and breach of international norms, based on their official function, as well as an entity involved in the novichok programme."
A statement from the Russian foreign ministry said that Germany and France "have now switched to threats and attempts to blackmail".
Mr Raab said the UK stands "side by side" with Germany and France.
He added: "On 6 October, the Organisation for the Prohibition of Chemical Weapons confirmed the findings from previous laboratory tests, that Alexei Navalny was poisoned by a military nerve agent of the novichok group, developed by Russia.
"The evidence is undeniable.
"The UK stands side by side with our German and French partners in our response to the abhorrent poisoning of Alexei Navalny."
He went on: "We will work together with our international partners to take forward sanctions targeting Russian officials and others who are considered responsible for this crime as well those involved in the development of the novichok chemical weapon programme.
"We will continue to work with the OPCW and all of our international partners to uphold the Chemical Weapons Convention and to hold Russia to account."