The academy - which runs the Oscars - said this was done in accordance with its standards of conduct.
TV star Cosby was convicted of sexual assault last month. Oscar-winning director Polanski admitted statutory rape of a 13-year-old girl in 1977.
Producer Harvey Weinstein was kicked out last year, following numerous allegations of sexual assault.
Less than a year after the downfall of the producer the #MeToo movement is catching up with other men who abused their power, the BBC's James Cook in Los Angeles reports.
Neither Cosby nor Polanski have publicly reacted to the academy's decision.
Cosby's wife, Camille, described his conviction as "mob justice, not real justice".
"This tragedy must be undone not just for Bill Cosby, but for the country," she said.
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