Nikolai Glushkov was found dead by his family and friends late Monday night and the cause of death is not yet determined.
The 68-year-old was a close friend of late Russian oligarch Boris Beresovsky, an opponent of Russian President Putin.
The Metropolitan Police said there was no evidence to suggest a link between the poisoning and Glushkov's death.
Police said the death was being treated as "unexplained", adding that the counterterrorism team would lead the investigation "as a precaution because of associations that the man is believed to have had".
Scotland Yard's Counter-Terrorism Command said it was investigating the death.
"At this stage the Met Police Counter Terrorism Command is leading the investigation as a precaution because of associations that the man is believed to have had. There is no evidence to suggest a link to the incident in Salisbury," the Met police statement said.
"A postmortem examination will be held in due course. The death is currently being treated as unexplained," it added.
In 1999, he was charged with money laundering and fraud and spent five years in a Russian jail before being freed in 2004 and after that fled to the UK.
Glushkov was granted political asylum and lived in London in recent years.
After his friend Berezovsky was found dead in 2013, Glushkov told the 'Guardian' that he doubted that the death was as a result of natural causes.
"I'm definite Boris was killed. I have quite different information from what is being published in the media," he had said.
In 2017, during a trial in absentia in Russia, Glushkov was sentenced to eight years in prison for allegedly stealing USD 123 million from Aeroflot.
According to Russian newspaper 'Kommersant', he was discovered with "signs of suffocation" by his family later on Monday.
His so-far unexplained death could add a further dimension to UK-Russian relations, which are under considerable strain after the poisoning of the 66-year-old Skripal with a deadly nerve agent.
The UK government had given the Kremlin until midnight yesterday to provide a "credible response", while Russia has denied any involvement and demanded access to the nerve agent in order to assist the investigation.
"President Trump said the US was with the UK all the way, agreeing that the Russian Government must provide unambiguous answers as to how this nerve agent came to be used," a Downing Street spokesperson said.
Meanwhile, Skripal and his 33-year-old daughter Yulia remain in a critical condition in hospital, where they have been since being discovered collapsed on a bench of a shopping centre in Salisbury on March 4.
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