Andrei Lugovoi and Dmitri Kovtun, two Russians identified as prime suspects by British police, are likely to have carried out the poisoning on the instructions of the Russian security services, the inquiry reported.
Although Prime Minister David Cameron called it a "state-sponsored action", his government did not announce sanctions in response, instead summoning Moscow's ambassador to London for talks lasting less than an hour.
Russia was sharply dismissive of the conclusions.
"Maybe this is a joke," Putin's spokesman Dmitry Peskov said. "More likely it can be attributed to fine British humour -- the fact that an open public inquiry is based on the classified data of special services, unnamed special services."
At the High Court in London, there were cries of "Yes!" as the main findings were read out.
Litvinenko's wife Marina, dressed in black and accompanied by her 21-year-old son Anatoly, embraced supporters afterwards.
She has spent years pushing for a public inquiry and had urged sanctions and a travel ban on Putin.
"I'm very pleased that the words my husband spoke on his deathbed when he accused Mr Putin of his murder have been proved true in an English court," she said.
She told AFP: "I can't say it is what I hoped for but I really appreciate it."
- 'Acting for a state body' -
Judge Robert Owen, the inquiry's chairman, said he was "sure" that Lugovoi and Kovtun placed polonium-210 in a teapot at the Millennium Hotel's Pine Bar, where they met Litvinenko on November 1, 2006.
"The FSB operation to kill Litvinenko was probably approved by Mr (Nikolai) Patrushev and also by President Putin," the report said.
Patrushev was the director of the FSB, the successor organisation to the Soviet-era KGB spy agency, at the time of the incident and has been a key security official since 2008.
Polonium-210 is a rare radioactive isotope only available in closed nuclear facilities.
The report, which contained classified evidence redacted from the version made public, said this suggested that Lugovoi and Kovtun "were acting for a state body rather than, say, a criminal organisation".
There was "no evidence" to suggest that either Lugovoi or Kovtun had any personal reason to kill Litvinenko and they were likely to be acting under FSB direction, Owen added.
Shortly after the report was published, London's Metropolitan Police issued a statement stressing they still wanted the pair to be extradited.
Owen said there were "powerful motives" for the killing. Litvinenko was seen as "having betrayed the FSB" and had regularly targeted Putin with "highly personal public criticism", including an accusation of paedophilia.
Litvinenko, an ex-KGB agent turned freelance investigator who also worked for British intelligence, accused Putin of ordering his killing in a statement before he died on November 23, 2006.
- 'Dangerous signal' -
In a statement to the House of Commons, Home Secretary Theresa May said Cameron would raise the findings with Putin.
She added that Britain would impose asset freezes on Kovtun and Lugovoi, but stressed the importance of Russia and Putin in efforts to resolve the conflict in Syria, a nod to the delicate timing of the issue for relations with Russia.
A US State Department spokesman said Washington was "deeply troubled" by the report's findings and that the perpetrators should be brought to justice.
Yet Britain's response to its conclusions fell short of the sanctions that some had called for.
Andy Burnham, interior affairs spokesman for the main opposition Labour Party, warned May she was sending "a dangerous signal to Russia that our response is too weak".
Jonathan Eyal, an analyst at the Royal United Services Institute think-tank, said the finding would make it difficult for Britain to "return to business as normal with Moscow".
"London also has to calculate whether this particular juncture when we need Russian support for a variety of operations in the Middle East for instance is the right moment to corner Moscow over this," Eyal said.
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Although Prime Minister David Cameron called it a "state-sponsored action", his government did not announce sanctions in response, instead summoning Moscow's ambassador to London for talks lasting less than an hour.
Russia was sharply dismissive of the conclusions.
"Maybe this is a joke," Putin's spokesman Dmitry Peskov said. "More likely it can be attributed to fine British humour -- the fact that an open public inquiry is based on the classified data of special services, unnamed special services."
At the High Court in London, there were cries of "Yes!" as the main findings were read out.
Litvinenko's wife Marina, dressed in black and accompanied by her 21-year-old son Anatoly, embraced supporters afterwards.
She has spent years pushing for a public inquiry and had urged sanctions and a travel ban on Putin.
"I'm very pleased that the words my husband spoke on his deathbed when he accused Mr Putin of his murder have been proved true in an English court," she said.
She told AFP: "I can't say it is what I hoped for but I really appreciate it."
- 'Acting for a state body' -
Judge Robert Owen, the inquiry's chairman, said he was "sure" that Lugovoi and Kovtun placed polonium-210 in a teapot at the Millennium Hotel's Pine Bar, where they met Litvinenko on November 1, 2006.
"The FSB operation to kill Litvinenko was probably approved by Mr (Nikolai) Patrushev and also by President Putin," the report said.
Patrushev was the director of the FSB, the successor organisation to the Soviet-era KGB spy agency, at the time of the incident and has been a key security official since 2008.
Polonium-210 is a rare radioactive isotope only available in closed nuclear facilities.
The report, which contained classified evidence redacted from the version made public, said this suggested that Lugovoi and Kovtun "were acting for a state body rather than, say, a criminal organisation".
There was "no evidence" to suggest that either Lugovoi or Kovtun had any personal reason to kill Litvinenko and they were likely to be acting under FSB direction, Owen added.
Shortly after the report was published, London's Metropolitan Police issued a statement stressing they still wanted the pair to be extradited.
Owen said there were "powerful motives" for the killing. Litvinenko was seen as "having betrayed the FSB" and had regularly targeted Putin with "highly personal public criticism", including an accusation of paedophilia.
Litvinenko, an ex-KGB agent turned freelance investigator who also worked for British intelligence, accused Putin of ordering his killing in a statement before he died on November 23, 2006.
- 'Dangerous signal' -
In a statement to the House of Commons, Home Secretary Theresa May said Cameron would raise the findings with Putin.
She added that Britain would impose asset freezes on Kovtun and Lugovoi, but stressed the importance of Russia and Putin in efforts to resolve the conflict in Syria, a nod to the delicate timing of the issue for relations with Russia.
A US State Department spokesman said Washington was "deeply troubled" by the report's findings and that the perpetrators should be brought to justice.
Yet Britain's response to its conclusions fell short of the sanctions that some had called for.
Andy Burnham, interior affairs spokesman for the main opposition Labour Party, warned May she was sending "a dangerous signal to Russia that our response is too weak".
Jonathan Eyal, an analyst at the Royal United Services Institute think-tank, said the finding would make it difficult for Britain to "return to business as normal with Moscow".
"London also has to calculate whether this particular juncture when we need Russian support for a variety of operations in the Middle East for instance is the right moment to corner Moscow over this," Eyal said.
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