The foundation and the prize are being paid for by The Enquirer and its publisher, American Media Incorporated, under a settlement of the lawsuit, said Judd Burstein, the lawyer for Mr. Katz. As part of the agreement, The Enquirer has also bought a full-page advertisement in the main news section of The New York Times on Wednesday. In it, The Enquirer says it was duped by a person claiming to be the same Mr. Katz. Mr. Burstein provided the text of the ad.

The amount of money being paid by The Enquirer will not be disclosed, Mr. Burstein said, adding, “It’s enough for the foundation to give out these grants for years to come.” On Tuesday, he formally filed papers to dismiss the lawsuit.

He noted that Mr. Katz did not receive or seek any personal payments. Mr. Katz, 48, said he was trying to figure out what a meaningful settlement would be to a person as demanding as Mr. Hoffman. “It’s so awful and ludicrous,” he said. “We had talked so often that 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.”

Besides Mr. Katz, the selection committee will include the writers Eric Bogosian, John Patrick Shanley and Jonathan Marc Sherman.

Mr. Katz said he and Mr. Hoffman met about 15 years ago through friends in the film world, but became close when their children wound up in the same Greenwich Village school. They would often stop for breakfast after the school drop-off, Mr. Katz said, and one of Mr. Hoffman’s favorite pictures was of the two of them in the Waverly diner in December 2011.

The actor’s final text messages were with Mr. Katz, inviting him to watch the second half of a Knicks game on the last evening of his life. Mr. Katz did not pick up the texts and respond until late that night, but he got no reply from Mr. Hoffman.

“The fact that he wanted me to come over for the Knick game meant that he did not want to be doing the drugs, because he never did them in my presence,” Mr. Katz said. “He once said to me, ‘Addiction is when you do the thing you really, really most don’t want to be doing.’ He was rigorously sober and had an awful relapse.”