Khodorkovsky, a former oil tycoon, was jailed for 10 years for financial crimes but pardoned over a week ago by President Vladimir Putin in a deal that Germany helped broker behind the scenes.
Russia's one-time richest man, who has said he would stay out of his home country, has been mulling a move to Switzerland where his wife Inna lives and his twin sons go to school, his spokeswoman said last week.
On Monday the Swiss foreign ministry and its embassy in Berlin confirmed Khodorkovsky, 50, had been granted a visa, without revealing any further details.
"Switzerland has granted the request of Mikhail Khodorkovsky for a Schengen visa. The visa allows a three-month stay in the Schengen area," said the statement, referring to a 26-country free-travel zone in Europe.
A spokesman for Khodorkovsky said: "He is very grateful to the Swiss authorities for the speed and efficiency with which they have dealt with his visa application.
"So soon after his decade of unjust imprisonment, Mr Khodorkovsky is delighted that Switzerland will be the second country in which he can breathe the air of freedom," he said in a statement on Khodorkovsky's website.
A Khodorkovsky spokeswoman later told AFP that he did not know exactly when he planned to travel to Switzerland, but added "probably after New Year's Day".
While still behind bars, Khodorkovsky said in an interview that "my family is my main treasure and we are together despite the years, kilometres and barbed wire".
He said he had seen lots of lonely people in prison and felt "ashamed" because he had a great family. "In the lottery of fate I won big time," he said, stressing his wife was waiting for him.
Khodorkovsky's supporters say the imprisonment was Putin's revenge against the former oil tycoon who financed the political opposition and openly criticized the Russian strongman Putin.
Last weekend Khodorkovsky told reporters in Berlin that he would not seek revenge against Putin and has pledged to help political prisoners held in Russian jails.