Two Russian men, Andrei Lugovoy and Dmitry Kovtun, have denied killing him.
The judge will decide whether to name any culprits and whether any elements in the Russian state were responsible.
BBC security correspondent Gordon Corera says the real issue for the report is whether the trail leads to the heart of the Russian state and even to President Vladimir Putin himself.
The report may also focus on whether it was specific investigations into links between organised crime and the Kremlin which led to Mr Litvinenko`s killing.
Our correspondent says that if it does point to state responsibility, pressure is likely to grow for the British government to take action against Moscow.
Speaking ahead of the inquiry`s findings, Mr Litvinenko`s son, Anatoly, told the BBC: "You want to find out who was behind the murder, who planned it, who commissioned it.
"That is why state responsibility is important to us."
The judge, Sir Robert Owen, heard from 62 witnesses in six months of hearings and was shown secret intelligence evidence about Mr Litvinenko and his links with British intelligence agencies.
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