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Cosby and Polanski are the first known members expelled for violating a conduct code the Academy adopted in December following intense public pressure from hundreds of accusations of sexual harassment or assault in the entertainment industry.
The Academy said in a statement its Board of Governors met on Tuesday and voted to remove Cosby and Polanski, who had been members since 1996 and 1969, respectively.
"The Board continues to encourage ethical standards that require members to uphold the Academy's values of respect for human dignity," the body whose 8,000 members vote on the Oscars said in the statement.
The expulsion comes as the entertainment industry grapples with misconduct allegations that have led to dozens of politicians, businessmen and entertainers stepping down or being dropped from creative projects, sparking the #MeToo social movement and the Time's Up campaign against workplace harassment and equal pay.
Polanski, 84, who won the best director Oscar in 2003 for "The Pianist," in 1977 admitted to having unlawful sex with a 13-year-old girl in Los Angeles.
The French-Polish director lives in France and fled the United States following pleading guilty for fear his deal with prosecutors would be overruled and he would get a lengthy prison term. Polanski's case is ongoing.
His attorney Harland Braun said Polanski was not given the chance to present his case before the Academy.
"It's just shocking that the Academy would expel someone without a fair hearing," Bruan said in a telephone interview.
In response, the Academy pointed to its conduct code, which says the board "retains its independent duty and authority ... to address and take action on any matter."
The Academy declined to say if Cosby and Polanski's convictions played a role in their expulsion.
A Cosby representative did not respond to a requests seeking comment.
Four Academy members are now known to have been expelled. Once powerful producer Harvey Weinstein was expelled in October after numerous women accused him of decades-long sexual misconduct.
Weinstein, 66, has denied having non-consensual sex with anyone.
Actor Carmine Caridi was expelled in 2004 for distributing copies of films that are sent to members.