The announcement came after Hoffman's longtime friend, New York playwright David Bar Katz, filed a $50 million lawsuit against the tabloid, which claimed the two men had a homosexual relationship.
Bar Katz said in court documents the story and an interview attributed to him were "complete fabrication."
The Enquirer withdrew the article and apologized, the Hollywood Reporter said. The publication also is funding Bar Katz's American Playwriting Foundation, which will grant $45,000 each year to make an unproduced play, as part of its settlement of Bar Katz's lawsuit.
Called the Relentless Award, the prize will represent "Hoffman's dogged pursuit of artistic truth," Bar Katz said.
The Enquirer also ran a full-page advertisement in the main news section of Wednesday's New York Times stating it was deceived by a person claiming to be Bar Katz, THR said.
Hoffman, the Oscar-winning star of "Capote," died this month in New York of a suspected heroin overdoe. The 46-year-old actor was survived by his longtime girlfriend and their three young children.