Paramount has agreed to pay President Trump $16 million to settle his lawsuit over the editing of an interview on the CBS News program “60 Minutes,” the company said late Tuesday, an extraordinary concession to a sitting president by a major media organization.

Paramount said its payment includes Mr. Trump’s legal fees and costs and that the money, minus the legal fees, will be paid to Mr. Trump’s future presidential library.

As part of the settlement, Paramount also agreed to release transcripts of “60 Minutes” interviews with eligible U.S. presidential candidates after such interviews have aired, subject to redactions as required for legal or national security concerns. The settlement does not include an apology.

The White House did not immediately respond to a request for comment.

Many lawyers dismissed Mr. Trump’s lawsuit as baseless and believed that CBS would ultimately prevail in court, in part because the network did not report anything factually inaccurate, and the First Amendment gives publishers wide leeway to determine how to present information.

But Shari Redstone, the chair and controlling shareholder of Paramount, told her board that she favored exploring a settlement with Mr. Trump. Some executives at the company viewed the president’s lawsuit as a potential hurdle to completing a multibillion-dollar sale of the company to the Hollywood studio Skydance, which requires the Trump administration’s approval.

The sale would end the Redstone family’s decades-long control of CBS News and Paramount Pictures and put it in the hands of David Ellison, the son of Larry Ellison, a tech billionaire who has backed Mr. Trump. Brendan Carr, the chairman of the Federal Communications Commission, has said that the president’s lawsuit against Paramount was not linked to the F.C.C.’s review of the company’s merger with Skydance. Paramount has also said that the two issues were unrelated.