The ruling was made after an agreement was reached between the Academy and Nate D Sanders, an auction house that specialises in movie memorabilia.
The golden statuette in question was awarded in 1942 to Joseph C Wright for his colour art direction on My Gal Sal.
His heirs sold the Oscar in June 2014.
The Academy tried to prevent the sale, claiming it breached a rule, instituted in 1951, that Oscar winners and their heirs cannot sell statuettes without first offering it to the organisation for $10.
The Academy's lawyers argued that Nate D Sanders was aware of the requirement when it bought the Oscar at a sale organised by Rhode Island firm Briarbrook Auctions.
Nate B Sanders previously handled the auction of 15 Oscar statues, a collection whose sale fetched more than $3m (Â£1.9m), in 2012.
"The Oscar is perhaps the world's most distinctive and prestigious award for achievement in the arts,'' said Gary E Gans, the lawyer who represented the Academy in the protracted litigation.
"This case established that the Academy can maintain the dignity and value of such an award by keeping it from becoming a commodity."
Last year the Academy took legal action against the heirs of another Oscar winner - cinematographer Robert Surtees - after they allegedly sold one of his awards on eBay.
An Oscar statuette that changed hands last year for $79,200 (Â£50,726) can be reclaimed by the Academy of Motion Picture Arts and Sciences for just $10 (Â£6.40), a Los Angeles judge has ruled.