Russia, which had declined to cooperate in the inquiry, described Britain's handling of the case as opaque and biased.
Litvinenko, 43, an outspoken critic of Putin who fled Russia for Britain exactly six years to the day before he was poisoned, died after drinking green tea laced with the rare radioactive isotope at London's Millennium Hotel.
An inquiry led by senior British judge Robert Owen found that former KGB bodyguard Andrei Lugovoy and another Russian, Dmitry Kovtun, carried out the killing as part of an operation probably directed by Russia's Federal Security Service (FSB), the main heir to the Soviet-era KGB.
"The FSB operation to kill Mr Litvinenko was probably approved by Mr Patrushev, then head of the FSB, and also by President Putin," Owen said.
"I have concluded that there is a strong probability that when Mr Lugovoy poisoned Mr Litvinenko, he did so under the direction of the FSB. I have further concluded that Mr Kovtun was also acting under FSB direction," he said.
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.
The British government said it would summon Russia's ambassador.
"The conclusion that the Russian state was probably involved in the murder of Mr Litvinenko is deeply disturbing," interior minister Theresa May told parliament.
"This was a blatant and unacceptable breach of the most fundamental tenets of international law and of civilized behavior."