Mr Litvinenko was poisoned after his dossier containing damaging details was deliberately leaked to the high-ranking Moscow figure, Mr Shvets told the BBC.
Mr Litvinenko died in London last month from suspected polonium-210 poisoning.
'Most probable theory'
In an exclusive interview, Mr Shvets told BBC Radio 4 programme The Litvinenko Mystery about his theory.
"I cannot really be 100% sure, but I am pretty sure," he said.
"Obviously there is always room for other suspicions, but in a tradecraft there is such a thing as most probable theory, and this is the one."
He said the British company wanted the eight-page dossier of commercial and political information before it invested millions of pounds in Russia.
Washington-based Mr Shvets, who advises businesses and individuals on legal and security issues in the former Soviet Union, said he talked to Mr Litvinenko in hospital.
Mr Litvinenko was convinced that he was poisoned when he met three Russians at the Millennium Hotel in London.
Mr Shvets said: "He drank a tea which was not made in front of him. He was agonised by the understanding that as a professional he failed.
"He was always saying 'I can identify my enemy a mile away'. But in this particular case, when it came to his own life, he failed."
Mr Shvets, who has been interviewed by senior Scotland Yard officers, said British detectives investigating the death now have the dossier compiled by Mr Litvinenko.