The settlement brings to a close a case that drew national attention over purported sexually compromising photographs involving the Falwells that could have been used as leverage against them. Michael Cohen, Mr. Trump’s former fixer who is now in prison, has said he intervened to help Mr. Falwell with the photos.

After Mr. Cohen’s involvement, the plaintiff, Jesus Fernandez Jr., said the case had forced him to change his name to Gordon Bello. His father, Jesus Fernandez Sr., who is no longer part of the lawsuit, became Jett Bello. The Bellos — then the Fernandezes — had filed the suit claiming the Falwells had promised them a share in the Miami Hostel. In a statement to The New York Times earlier this year, the senior Mr. Bello would not further explain the name changes, citing the pending litigation.

Mr. Falwell has denied the existence of the photographs, which Mr. Cohen discussed with the actor Tom Arnold, an anti-Trump crusader, in a secret recording. In legal filings, the Falwells denied ever promising the Fernandezes a share of the ownership of the hostel, which rents beds for as little as $15 a night.

The $4.7 million cash purchase of the hostel and its building — including a $1.8 million loan from the Falwells, according to a sworn affidavit — was a business venture with Giancarlo Granda, whom the couple befriended poolside at a Miami Beach hotel, the Fontainebleau, in 2012. Mr. Granda consulted a high school friend, the junior Mr. Bello, whose father had worked in Miami real estate for decades. (Mr. Falwell, who is not a minister, spent years as a lawyer and real estate developer.)

By the time the court case reached an impasse in late 2015, the fight had turned to the photos, several people involved in the case told The Times earlier this year. One or more people among Mr. Granda, the Bellos and their lawyers were believed to have the photos in their possession.