43-year-old Litvinenko, a former agent in the Russian federal security service (FSB) or secret police, died days after being poisoned with radioactive polonium-210 which he is believed to have drunk in a cup of tea.
The finding by Robert Owen, a retired High Court judge, in a 328-page report represented by far the most damning official link between Litvinenko's death and the highest levels of the Kremlin.
There is a "strong probability" they were acting on behalf of the Russian FSB secret service, the inquiry found.
Two Russian men, Andrei Lugovoi and Dmitry Kovtun, have been accused of his murder. They deny killing him.
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Owen said that taken as a whole the open evidence that had been heard in court amounted to a "strong circumstantial case" that the Russian state was behind the assassination.
But when he took into account all the evidence available to him, including a "considerable quantity" of secret intelligence that was not aired in open court, he found "that the FSB operation to kill Litvinenko was probably approved by [Nikolai] Patrushev [head of the security service in 2006] and also by President Putin".
British Prime Minister David Cameron's official spokeswoman said Downing Street was taking the findings "extremely seriously" and that the Prime Minister found them "extremely disturbing".
The spokeswoman said: "The conclusion that the murder was authorised at the highest levels of the Russian state is extremely disturbing. It is not the way for any state, let alone a permanent member of the UN Security Council, to behave.
The spokeswoman said measures taken against Russia in 2007 remained in place, adding: "In the light of the inquiry's findings, we are considering what further action we should take."
In Moscow, Russian Foreign Ministry spokeswoman Maria Zakharova said, "We regret that a purely criminal case was politicised and darkened the general atmosphere of bilateral relations.