The $45,000 bursary was suggested by Philip Seymour Hoffman’s friend David Katz, who sued The National Enquirer over an article about their friendship.
The story was printed just days after Philip Seymour Hoffman’s death earlier this month and subsequently retracted.
David Katz’s lawyer said the prize would be funded “for years to come”.
David Burnstein told the New York Times that David Katz, who is a playwright, wanted the undisclosed settlement to be used positively, and had set up the American Playwriting Foundation as a result.
He said he had spoken often with Philip Seymour Hoffman about how “it’s a tragedy playwrights can’t survive being playwrights – about how nice it would be if you could make your rent and still have an occasional steak”.
The annual prize will be known as the Relentless Award, in a nod to Philip Seymour Hoffman’s pursuit of artistic truth and integrity.
A panel of four theatre writers, including David Katz, will form a selection committee to choose the recipient of the bursary, whose work must be previously unproduced.
The National Enquirer published a story making allegations about the relationship between Philip Seymour Hoffman and David Katz, asserting that the two men took drugs together.
David Katz said Philip Seymour Hoffman never took drugs in his presence and that he had never spoken to the publication.
The National Enquirer removed the story and contended they had been given their information by another David Katz, who claimed that he was the playwright.
As well as the libel settlement, the magazine is due to publish a full-page apology in the New York Times.
David Burnstein said the man claiming to be David Katz would also face a legal challenge.
Philip Seymour Hoffman died at the age of 46 following a drugs overdose at his New York apartment on February 2.
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