Zbigniew Ziobro, Poland's attorney general and minister of justice, will submit his appeal to the Supreme Court, his spokesman told CNN.
In October, a Polish court rejected a U.S. extradition request
U.S. officials have pursued Polanski's extradition for decades, seeking to bring him to account for underage sex with a 13-year-old girl in California in 1977 when the director was 43.
Polanski pleaded guilty at the time under a deal with prosecutors that included dropping more serious charges.
But he fled before he could be sentenced after learning the judge in the case might impose a stricter sentence than he had anticipated.
Attorney general favors extradition
Polish officials agreed to consider the U.S. extradition request after Polanski attended a museum opening in 2014 in Poland, where he grew up and has visited frequently.
According to an extradition agreement between Poland and the United States, the 82-year-old Polanski is eligible for extradition, Ziobro's spokesman said.
Ziobro, who has been a critic of the decision not to extradite the filmmaker, announced his decision to appeal on Polish public radio Tuesday.
In rejecting the extradition request in October, Polish Judge Dariusz Mazur took the director's age into account, saying that agreeing to the U.S. request would result in "unlawful deprivation of freedom ... possibly in difficult and unsuitable conditions for an elderly person."
Fugitive from U.S. justice
The pending appeal reignites a controversy that has followed the director, who has French and Polish citizenship, for decades.
In 1977, Polanski was accused of giving the victim champagne and part of a Quaalude tablet before having sex with her during a photo shoot at actor Jack Nicholson's house, when she was five years below the age of consent.
He was charged with a number of felonies, including rape and sodomy, but prosecutors dropped those charges in a plea bargain that saw him plead guilty to unlawful sex with a minor.
He subsequently fled the country in 1978, continuing his career as a Hollywood exile in countries where he would not face potential extradition. In 2003, he was a no-show at the Academy Awards ceremony where he won an Oscar for his film "The Pianist."
Victim wants matter dropped
The victim, who years ago identified herself as Samantha Geimer, has said she was taken advantage of and made to have sex.
But she has publicly forgiven Polanski and urged that the matter be dropped.
"Every time this case is brought to the attention of the court, great focus is made of me, my family, my mother and others," Geimer said in court papers filed in 2009.
"That attention is not pleasant to experience and is not worth maintaining over some irrelevant legal nicety, the continuation of the case."
Authorities in Canada, France, Israel, Thailand and Switzerland have previously declined to extradite the director, who lives in France.