Polanski can now start making a planned film in Poland, his legal team said.
The Oscar-winner now lives in France.
The 82-year-old won an Oscar in 2003 for his film The Pianist.
Polanski has French and Polish citizenship. He lives in France - which does not extradite its own citizens.
Polanski, who admitted unlawful sex with a minor - statutory rape - fled the US ahead of sentencing in 1978.
His Polish lawyers had argued against his extradition, citing claimed legal flaws in the US process and the 42 days Polanski served in prison at the time, according to the Associated Press news agency.
Polanski grew up in Poland and is regarded as one of the country`s greatest living artists.
He wants to make a film about the 19th-Century Dreyfus Affair, a French scandal in which an army officer was wrongly convicted of treason. The affair exposed anti-Semitism in French society.
The crime victim, Samantha Geimer, has said she would prefer it if the US case against Polanski were dropped.
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