Berman was found with a gunshot wound to the back of her head in her Benedict Canyon home on Christmas Eve.
The charges come after two years of investigations that led authorities to believe Durst lay in wait with a gun and murdered a witness. These special circumstances mean he is eligible for the death penalty.
Durst was arrested Saturday at a New Orleans hotel on a capital murder warrant issued by the Los Angeles Police Department for Berman's murder. At the time of his arrest, authorities found him in possession of a revolver.
In addition to the murder charge, a Louisiana State Police trooper said the 71-year-old millionaire has been booked on weapons charges.
An arrest warrant was issued for Durst and he was rebooked in to the Orleans Parish Jail on Monday. He now faces charges for a convicted felon in possession of a firearm and possession of a weapon with a controlled dangerous substance. According to Trooper Melissa Matey, Durst was carrying a small amount of marijuana.
Durst also waived extradition to return to Los Angeles to face charges for the December 2000 murder. Matey said it is unclear if Louisiana prosecutors will try to keep Durst in the state for those charges before he heads to California.
On Sunday, an HBO documentary series "The Jinx: The Life and Deaths of Robert Durst" ended with Durst making a startling statement.
During a tense interview regarding the similarities between his handwriting and an anonymous letter that alerted police to Berman's death, Durst stepped away to the bathroom still wearing the live microphone.
"There it is. You're caught!" he whispered to himself. "What the hell did I do? Killed them all, of course."
A source with the LAPD said an anonymous caller tipped off the department after watching the show and that the tip led the department to Durst. In addition to the tip, FBI agents had separate information showing that he was traveling from Texas to New Orleans. Once he was spotted at the hotel, he was arrested.
Loyola Law School professor Laurie Levenson said that recording is admissible in court.
"If they had not made a documentary, you would have thought that this script is too bizarre even for a movie," she said. "Durst's comment in the bathroom is absolutely admissible. No one forced him to say it. The question is, how much is it worth? Because he'll say, 'I didn't really mean it. I was just repeating what other people were saying.'"
The bathroom recording could become evidence in Berman's murder trial.
Filmmakers of "The Jinx" said Durst knew he was being recorded throughout the making of the series, and that they shared any evidence they found with authorities before broadcasting the documentary on HBO.
The six-part series profiled Durst's connections to three different murders: his wife Kathleen, Berman and neighbor Morris Black in 2001.
Kathleen Durst disappeared on Jan. 31, 1982. Her body was never found and she was declared dead in 2001. Her husband was never charged in connection to her disappearance, but four of her friends believe he was somehow involved.
Kathleen had said to friends, "if anything ever happens to me, don't let Bobby get away with it" in the months and weeks leading up to her disappearance.
In 2003, Durst was acquitted by a Texas jury for the murder of Black, whose body parts were found floating in Galveston Bay. He had fled Texas and was brought back for the murder trial after he was caught shoplifting in Pennsylvania.
During the trial, Durst's lawyers said he killed Black in self-defense, but he admitted to using a paring knife, two saws and an ax to dismember the body and dispose of it.
In 2004, Durst pleaded guilty to two state charges of bail jumping and one count of tampering with evidence. That same year he also pleaded guilty in federal court in Pennsylvania to two firearm counts.
According to authorities, Berman was going to speak with New York police about the disappearance of Kathleen Durst.
In the criminal complaint filed against Durst on Monday, it states Berman was a witness to a crime and that she was "intentionally killed because of that fact."
Durst's attorney Dick DeGuerin said his client is "ready to end all the rumor and speculation and have a trial."
Levenson said the defense could easily shoot down Durst's shocking comments said in the documentary.
"But on the defense side, they're going to start pointing out all the things that the prosecution does not have. They don't have the DNA evidence that we know about. They don't have eyewitnesses. They don't have an actual confession. They have a few words," she said.
In case the recording is used in court, "The Jinx" director Andrew Jarecki and co-writer Marc Smerling released a statement.
"Given that we are likely to be called as witnesses in any case law enforcement may decide to bring against Robert Durst, it is not appropriate for us to comment further on these pending matters. We can confirm that evidence (including the envelope and the washroom recording) was turned over to authorities months ago," the statement said.
Durst is being held without bail in New Orleans. He will be brought back to Los Angeles for his arraignment at a future date, according to the Los Angeles County District Attorney's Office.
The case remains under investigation by the LAPD.
The Associated Press and ABC News contributed to this report.