Russian prison officials said Mr Khodorkovsky, 50, had requested travel papers to see his sick mother there.
Mr Khodorkovsky’s father told AP he and his wife were still in Moscow but were planning to fly to Germany, where she has been treated in the past.
Mr Putin earlier said he had signed the pardon on “the principles of humanity”.
Mr Khodorkovsky, the former head of the now defunct oil giant Yukos and once Russia’s richest man, had been jailed for tax evasion and theft after funding opposition parties.
Mr Khodorkovsky left the penal colony where he was being held, in the Karelia region of north-western Russia, early on Friday afternoon.
Russia’s Federal Penal Service, quoted by news agency Interfax, said: “In the course of his release, Khodorkovsky asked for a passport for foreign travel. His request was met.
“Once he was released from prison, he left for Germany, where his mother is undergoing treatment.
“We stress that the flight took place at his request and his exit documents were processed at his personal request.”
The German foreign ministry later confirmed that Mr Khodorkovsky had landed at Schoenefeld airport in Berlin, after the German embassy in Moscow had facilitated his departure from Russia.
A representative of the German foreign ministry was at the airport to meet him.
Mr Khodorkovsky reportedly flew on a private jet from St Petersburg.
The Associated Press (AP) quoted a spokesperson for the energy consulting firm, OBO Bettermann, as saying that former German foreign minister Hans-Dietrich Genscher had asked the company to provide a plane.
Mr Khodorkovsky’s mother, Marina, 79, has been treated in Germany before.
However, Mr Khodorkovsky’s father, Boris, told AP that he and his wife were still in Moscow and were planning to fly to Germany on Saturday.
Reuters quoted Mr Khodorkovsky’s mother as saying she was waiting in Moscow and would leave Russia to see him if necessary.
Mr Khodorkovsky was jailed after being convicted of stealing oil and laundering money in 2010.
He had been in prison since 2003 when he was arrested and later convicted on charges of tax evasion. He was due to be released next August.
The presidential pardon came after Russian MPs on Wednesday backed a wide-ranging amnesty for at least 20,000 prisoners.
Mr Putin confirmed it would apply to the two members of punk band Pussy Riot still in prison and Greenpeace activists detained for their protest at a Russian oil rig in the Arctic.
Analysts say Mr Putin may be trying to ease international criticism of Russia’s human rights record ahead of February’s Winter Olympics in Sochi.