The mystery over Natalee Holloway‘s famous disappearance was cleared up once and for all — because the prime suspect just admitted he killed her and attempted to defraud her family.

Joran van der Sloot appeared in an Alabama court Wednesday, where prosecutors told the court van der Sloot had confessed to Holloway’s parents that he’d taken her life … apparently, he bludgeoned her to death after she refused his sexual advances — this according to Holloway’s mother, Beth, who also spoke.

She said, “You didn’t get what you wanted from Natalee, your sexual satisfaction, so you brutally killed her” — adding that he “terminated her dreams, her potential, her possibilities.”

Beth says van der Sloot admitted to killing Natalee on the beach and putting her body in water.

Van der Sloot entered a guilty plea to charges of wire fraud and extortion that he was facing here in the U.S. case — while indirectly tied to Holloway’s death — was inextricably linked to her disappearance.

Interestingly enough, van der Sloot expressed remorse for the killing, saying he’d become a born-again Christian — but Holloway’s mother, as she told him that he’d always be a killer … no matter what.

While van der Sloot might’ve copped to killing Holloway — that’s not what he’ll be punished for here in the U.S. The case is somewhat convoluted — especially since she first vanished almost 20 years ago on the island of Aruba — but basically … officials in America ended up charging him for attempting to sell information to Holloway’s family about where her remains are … which Beth says she actually paid for out of desperation.

As part of this plea deal he struck with the prosecution, van der Sloot was forced to finally clear up the details of Holloway’s disappearance in 2005 … and now he has.

Holloway — who was 18 — was on a high school graduation trip in the Dutch territory … and witnesses say they saw her leaving a bar with van der Sloot and two other men, who have long been suspected to have been involved in whatever it is that happened to her.

The 3 men were arrested a couple different times over the years in connection to Holloway’s disappearance — but they were also cut loose over a lack of evidence. Van der Sloot, however, is the one who’s fallen into the crosshairs of the U.S. … as they indicted him in 2010, alleging he’d tried extorting and defrauding the Holloway family.

While he was charged in America well over a decade ago, he hadn’t gotten extradited until just earlier this year — as part of an agreement with the Peruvian government. You see, he’s actually serving a prison sentence there for an entirely different case … where a court found him guilty of murdering a different young woman, Stephany Flores.

Anyway, once this is dealt with, he’ll reportedly be shipped back to Peru to finish his sentence — and, after that, presumably return to America to start serving whatever punishment he receives as part of this case.

The Holloway story was one of the biggest disappearance cases in recent memory — and her family had her declared legally dead in 2012 after many years of going without answers.

The Holloway family’s attorney says that after van der Sloot’s statements in court about the disappearance, there will be no further searches for the teen’s remains … something her family has long sought.