His spokesman says Khodorkovsky and his wife travelled by train to Basel from Germany to accompany their two sons who are returning to their Swiss school.
Khodorkovsky flew to Germany after his release on 20 December.
He served 10 years in jail for fraud and tax evasion, but insists that his conviction was politically motivated.
While travelling to Basel on Sunday, Khodorkovsky told Swiss TV he wanted to campaign for the release of prisoners.
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"You can't remain quiet when you know that political prisoners languish in jail," he said.
"I think campaigning for the release of those who have been jailed without justification is the job of every ordinary citizen. As far as I'm concerned, it has nothing to do with politics," he added.
Khodorkovsky has not yet decided whether he wants to stay permanently in Switzerland, his spokesman said.
The businessman made his fortune from the controversial privatisation of Soviet state assets. In 1995, he acquired oil giant Yukos.
After President Vladimir Putin came to power Khodorkovsky made no secret of his support for the liberal opposition,
In 2005 he received an eight-year jail sentence for tax evasion, fraud and embezzlement. Two years before his release date he was convicted again on further charges of embezzlement and money laundering.
He had been due to be released next August, but requested a pardon because his mother is suffering from cancer.
The pardon came after Russian MPs backed a wide-ranging amnesty for at least 20,000 prisoners.
Two members of punk protest band Pussy Riot - jailed for staging a protest in a cathedral - have also recently been freed.
Analysts say Mr Putin may have been trying to dampen international criticism of Russia's human rights record ahead of February's Winter Olympics in Sochi.
Ex-oil tycoon Mikhail Khodorkovsky, who was freed from a Russian jail last month, has arrived in Switzerland where he has been granted a three-month visa.