Mr Navalny became ill during the flight and the plane made an emergency landing in Omsk. Russian officials were persuaded to allow him to be airlifted to Germany two days later.
After tests confirmed poisoning with a Novichok nerve agent, the EU demanded a "transparent" investigation by the Russian government. "Those responsible must be brought to justice," a statement read.
UK Prime Minister Boris Johnson condemned the poisoning as "outrageous".
In an Instagram post on Tuesday, Mr Navalny rubbished suggestions - purportedly from President Putin - that he had poisoned himself.
French newspaper Le Monde reported that in a telephone call with President Emmanuel Macron on 14 September, Mr Putin had spoken "with contempt about Alexei Navalny, considering him a simple internet troublemaker who had simulated diseases in the past".
"Putin has outsmarted me," Mr Navalny wrote on Instagram, mocking the Russian president. "He is nobody's fool. As a result, I, like a fool, spent 18 days in a coma but failed to achieve what I wanted. The provocation has failed!"
Western politicians are still undecided over their response to the poisoning, says the BBC's Jenny Hill in Berlin.
However, Mr Navalny's discharge from hospital will intensify pressure on German Chancellor Angela Merkel who has demanded - so far in vain - a full explanation from the Kremlin, she adds.
A nerve agent from the Novichok group was also used to poison Russian ex-spy Sergei Skripal and his daughter in Salisbury, England in 2018. They both survived, but a local woman, Dawn Sturgess, died after coming into contact with the poison.
Britain accused Russia's military intelligence of carrying out that attack. Twenty countries expelled more than 100 Russian diplomats and spies. Moscow denied any involvement.
BBC