Litvinenko, a former KGB agent who had become a fierce Kremlin critic in exile, met Lugovoy and Dmitry Kovtun, another Russian businessman, at the Pine Bar of London's Millennium Hotel on November 1 last year.
Within hours, he had fallen severely ill. He suffered an agonising death over the next three weeks as his organs gradually failed, his hair fell out and images of his emaciated body were published around the world.
|Litvinenko died last year after|
being poisoned with Polonium 210 [AP]
Doctors eventually diagnosed polonium poisoning.
In a letter dictated on his deathbed, Litvinenko, who had acquired British citizenship weeks before he was poisoned, accused Vladimir Putin, the Russian president, of his murder.
Moscow dismissed the accusation as ridiculous.
It has launched its own investigation into Litvinenko's death and denies that its security services played any part.
Lugovoy, a former KGB bodyguard who later worked as head of security for Boris Berezovsky, a businessman, has previously laughed off reports Britain would seek his extradition.
He has denied killing Litvinenko and accused British media of demonising him.
Lugovoy was not answering calls on Tuesday and did not respond to messages sent to his cellular telephone.
Ken Macdonald, head of the CPS, said prosecuting him would clearly be in the public interest.
"I have instructed CPS lawyers to take immediate steps to seek the early extradition of Andrei Lugovoy from Russia to the United Kingdom, so that he may be charged with murder - and be brought swiftly before a court in London to be prosecuted for this extraordinarily grave crime," he said.
Susan Hemming, a CPS spokeswoman, said it would ask the police to obtain an arrest warrant, which would then be sent to Russian authorities.
"The ball is now in the Russians' court," Hemming said. "We can't speculate on what the Russians will do."
Marina, Litvinenko's widow, said: "I am now very anxious to see that justice is really done and that Mr Lugovoy is extradited and brought to trial in a UK court."