But the Swiss Justice Ministry says it will keep Polanski in jail until it decides whether to appeal his release to the country's supreme court.
Spokesman Folco Galli says the ministry will make its decision "quickly," even though it has 10 days to appeal.
The Swiss Criminal Court still considers Polanski a high flight risk. Its ruling Wednesday said the new bail offer was significant enough to offset those concerns.
The decision does not affect the Swiss government's ongoing assessment of whether it should extradite Polanski to the U.S. for having sex in 1977 with a 13-year-old girl.
"The key here is house arrest and electronic monitoring, which would put a crimp in his plans to flee the jurisdiction. And remember, under Swiss law, Polanski hasn't committed a crime," said CBS News legal analyst Andrew Cohen.
"He's being released from prison but not from confinement and not from the country and if he tries to skip out now he'll have both Swiss and U.S. officials trying to track him down," Cohen said.
"I am sure we will see an appeal here, and a strong request by American officials for a reversal of this decision. But ultimately it's a matter for the Swiss courts and Swiss law," Cohen added.