In 2005, an American teenager, Natalee Holloway, disappeared on a senior high school class trip to Aruba. Her case inspired countless hours of cable TV programming, more than half a dozen nonfiction books, multiple episodes in the “Law & Order” franchise and at least one stage production. The obsessive attention stoked a backlash of media criticism.

On Wednesday, the man long suspected of killing her, Joran van der Sloot, finally admitted his brutal crime in a statement presented to a federal judge in Birmingham, Ala. It had taken 18 years, as long as her short life.

Suspicion had fallen early on Mr. van der Sloot, a Dutch student who was among three people seen leaving a nightclub with her in the early hours of May 30, 2005.

He was arrested twice, but never charged in connection with Ms. Holloway’s disappearance or death, and despite an extensive search, her remains have never been found. She was declared legally dead in 2012. No one has ever been charged in her killing.

Mr. van der Sloot, 36, is serving a 28-year prison sentence in Peru for the 2010 murder of a 21-year-old student. His admission in the Holloway case came as he was pleading guilty to charges that he had tried to extort money from her mother, Beth Holloway.

At a news conference after the hearing, Beth Holloway said his confession had brought her family’s long ordeal to an end. “As far as I am concerned it’s over. It’s over,” she said, adding, “I’m satisfied knowing that he did it, he did it alone and he disposed of her alone.”

“He is the killer,” she said, adding, “He described when and how he killed her.”

The charges stemmed from 2010 when Mr. Van der Sloot tried to demand a $250,000 payment from Beth Holloway, claiming to have knowledge of the location of her daughter’s remains, prosecutors said. He received only $25,100 from her after providing false information, according to prosecutors.

In exchange for a 20-year sentence for charges of extortion and wire fraud, Mr. van der Sloot had agreed to provide “full, complete, accurate, and truthful information” about the disappearance of Natalee Holloway.

Documents released Wednesday by the U.S. District for the Northern District of Alabama as part of the plea agreement included his account, for the first time, of what happened that night in Aruba, the Caribbean island nation and former Dutch colony where Mr. van der Sloot was living at the time.

In excerpts from a statement that Mr. van der Sloot gave on Oct. 3 to his lawyer, Kevin Butler, he described brutally attacking Ms. Holloway on the beach after she rejected his sexual advances.

He described wanting to be dropped off with Ms. Holloway a distance from the hotel where she was staying with more than 100 recent graduates of Mountain Brook High School in Alabama so he “might still get a chance to, to be with her.” He said they began kissing while lying on the beach, but she refused further sexual advances.

When he persisted, he said, she kneed him in the crotch, and he kicked her “extremely hard” in the face. At that point, he said, she was “possibly even, uh, even dead but definitely unconscious.”

Then, he said, he picked up a large cinder block and used it to “smash her head in with it completely.”

He brought her to the ocean’s edge in a “half pull and half walk,” wading in up to his knees. He pushed her into the water, he said, and then walked home.

At the sentencing, Judge Anna M. Manasco told Mr. van der Sloot, “You have brutally murdered, in separate instances years apart, two young women who refused your sexual advances,” according to The Associated Press.

Mr. van der Sloot was extradited from Peru in June. He will have to return there to finish serving his sentence for the 2010 murder of the student, Stephany Flores, as well as another for a drug trafficking charge. He will serve his sentence on the federal extortion and wire fraud charges concurrently with the sentence he is serving in Peru.

When the news of Ms. Holloway’s disappearance first broke in 2005, cable news networks were criticized for devoting hours of airtime to the case of an attractive young white woman from an affluent suburb of Birmingham, while other cases involving women from other ethnic groups and backgrounds went uncovered.

One critic, Matthew Felling of the Center for Media and Public Affairs, said at the time that the Holloway coverage amounted to “emotional pornography.”

But the public fascination continued. A Lifetime movie, titled simply “Natalee Holloway,” set a ratings record for the network in 2009. Other television movies and true-crime productions followed, including one, “Vanished with Beth Holloway,” hosted by Ms. Holloway’s mother.

In 2008, a Dutch crime reporter, Peter R. de Vries, organized a sting operation for his television show in which he tried to solve the case using an informer and hidden cameras. Stopping just short of an outright confession on the program, Mr. van der Sloot told the informer that Ms. Holloway was “never to be found.”

Speaking to reporters after the hearing on Wednesday, Beth Holloway said that her daughter, who vanished days after her high school graduation, would now be 36 years old.

“It’s been a very long and painful journey,” she said, “but we finally got the answers we’ve been searching for, for all these years. We got justice for Natalee.”

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