Robert Durst was recorded saying in private that he had "killed them all", soon after being asked in an interview about the death of a friend in 2000.
The 71-year-old has always maintained his innocence in Susan Berman's murder.
Mr Durst agreed to be transferred from New Orleans to Los Angeles, where he will face a first-degree murder charge.
Prosecutors are also reportedly tying the case to the unsolved disappearance of his first wife, Kathleen, in 1982.
She went missing after spending the weekend at their country home in New York State and was eventually pronounced legally dead.
In 2001, Mr Durst was acquitted of murder. He convinced a Texas jury that he had shot and killed elderly neighbour Morris Black in an act of self-defence. Mr Durst admitted to dismembering his body and dumping it in Galveston Bay.
Mr Durst's estranged family said they were "relieved and also grateful to everyone who assisted" in his arrest.
The family control one of New York's largest real estate empires and are believed to be worth at least $US4 billion.
FBI agents acting on an arrest warrant issued by Los Angeles prosecutors arrested Mr Durst as he walked into a hotel in New Orleans where he had checked in under a false name.
He was remanded in custody pending a hearing on Monday.
His lawyer Chip Lewis said his client would continue to maintain his innocence.
Los Angeles police said the arrest resulted from "investigative leads and additional evidence that has come to light in the last year".
But Mr Lewis said he had no doubt the arrest was orchestrated in co-ordination with an HBO documentary, The Jinx: The Life and Deaths of Robert Durst, which included a lengthy interview with Mr Durst.
The final episode, broadcast on Sunday night, included what appeared to be a confession to the killings of Ms Berman, Mrs Durst and Mr Black.
According to the filmmakers, Mr Durst was still wearing a wireless microphone when he went into a hotel bathroom after the interview.
"There it is, you're caught," he whispered to himself. "What the hell did I do? Killed them all, of course."
It is not known if he is speaking sincerely, but it came after he was asked whether he had written a letter only Ms Berman's killer could have sent.
Last July, Mr Durst was charged with criminal mischief after allegedly urinating on a display in a pharmacy in Houston.
Five months later, he appeared in court in New York on charges of trespassing on property belonging to his family. The Durst Organization owns 11 skyscrapers in Manhattan, including One World Trade Centre.
Mr Durst formally cut ties with his family and the company in 2006 in return for a settlement of about $US65 million.