Litvinenko, 43, an outspoken critic of Putin who fled Russia, died after drinking green tea laced with the rare radioactive isotope polonium-210 at London's plush Millennium Hotel.
An inquiry led by senior judge Robert Owen found that former KGB bodyguard Andrei Lugovoy and fellow Russian Dmitry Kovtun carried out the poisoning as part of an operation directed by Russia's Federal Security Service (FSB), the main heir to the Soviet-era KGB.
"Taking full account of all the evidence and analysis available to me, I find that the FSB operation to kill Mr Litvinenko was probably approved by Mr Patrushev and also by President Putin," the inquiry said.
Nikolai Patrushev was formerly head of the FSB.
"I am satisfied that in general terms members of the Putin administration, including the President himself and the FSB, had motives for taking action against Mr Litvinenko, including killing him in late 2006," the inquiry said.
The Kremlin has always denied any involvement. From his deathbed, Litvinenko told detectives Putin had directly ordered his killing.
The death of Litvinenko marked a post-Cold War low point in Anglo-Russian relations, and ties have never recovered, marred further by Russia's annexation of Crimea and its support for Syrian President Bashar al-Assad.
Both Lugovoy and Kovtun have previously denied involvement and Russia has refused to extradite them. Lugovoy was quoted by the Interfax news agency as saying the accusation was absurd.
Litvinenko's widow 'pleased' with British inquiry findings
The widow of Alexander Litvinenko, the former KGB spy murdered in Britain welcomes an inquiry conclusion that Putin probably approved his killing by radioactive poisoning. Marina Litvinenko is now calling for British Prime Minister David Cameron to take action against Russia.
"I am of course very pleased that the words my husband spoke on his death bed when he accused Mr Putin of his murder have been proved true in an English court with a high standard of independence and fairness," she says.
"But now it is time for David Cameron, I am calling immediately for exclusion from the UK of all Russian intelligence operatives whether from FSB who murdered Sasha or from other Russian agencies based in the London embassy."
Russian foreign ministry calls Britain's Litvinenko inquiry biased
The Russian Foreign Ministry on Thursday dismissed the outcome of a judge-led British inquiry into the 2006 killing of former KGB agent Alexander Litvinenko as biased and opaque, saying London's handling of the case had
clouded bilateral ties.
Maria Zakharova, a spokeswoman for the foreign ministry, accused Britain of politicising the matter.
"We regret that what was a purely criminal case was politicised and has clouded the general atmosphere of our bilateral ties," she told reporters.
"The process ... was not transparent for the Russian side or for society because of the way materials were examined behind closed doors under the pretext that they were secret."
She said the final outcome was therefore the result of a "politically-motivated and extremely opaque process".
