Khodorkovsky applied for a three-month visa shortly after his December 20 arrival in Berlin, following his pardon by Russian President Vladimir Putin and release from decade-long imprisonment.
Embassy spokeswoman Alexandra Baumann said the application has now been approved. It allows him to travel freely within the 26-nation Schengen area, which includes Switzerland and most of the European Union but not Britain.
The German government gave Khodorkovsky a one-year visa for Germany following his release.
Khodorkovsky's sons go to school in Switzerland, and he has business ties there.
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Russia's pardon of Khodorkovsky, along with an amnesty that brought the release of the remaining members of punk band Pussy Riot and of Greenpeace activists detained since September, has been widely seen as part of an attempt to soothe criticism of the country's human rights record before the Winter Olympics in Sochi, Russia, in February.
Khodorkovsky has business ties to Switzerland stretching back to his days as head of the Yukos oil company. When Khodorkovsky was prosecuted for tax evasion and money-laundering, Russian officials sought to seize about USD 5 billion linked to Yukos that had been deposited in Switzerland.