But the investigation remains open, police said.
Last month, the LAPD said it was conducting tests on a knife that was purportedly found at Simpson's old property. Police said in March that they recently recovered the knife from a retired LAPD officer.
The officer, identified by his lawyer as George Maycott, retired in 1998 and was working security on a movie set about five years later when he was approached by a construction worker down the street from Simpson's demolished estate, attorney Trent Copeland said last month.
The worker handed him a knife with no evidence of blood and Maycott immediately called the LAPD, Copeland said. According to Copeland, Maycott was put on hold and was later told that the Simpson case was over.
Maycott then took the knife home and put it in his toolbox, where it sat for about 15 years, Copeland said. The knife was taken into custody by police on Feb. 10.
The LAPD said last month that it was looking into the retired officer's story. The LAPD said the knife was submitted to the lab to be studied for forensics including DNA and hair samples.
Copeland told ABC News today that Maycott feels vindicated and is "relieved that the process is now over."
"Because what he said from the start turned out to be true," Copeland said. "Although this was a knife that was allegedly found on the property, it was clearly not the knife connected to the murders.”
Copeland said Maycott's "good name" has been dragged through the mud but that the retired officer holds no grudges against the LAPD.
"This is a retired police officer, a 70 year old man, who didn’t ask for this attention and did what he thought was the right thing back in 2003. And that was to call the LAPD and to let them know that he had a knife that was allegedly recovered on the property," Copeland said. "And the fact that they chose not to act on that... can't be directed negatively towards him."
There have been previous reports of a knife found near Simpson's old home.
The Associated Press reported in May 1998 that a construction crew found a folding-blade knife in Simpson's neighborhood but police said at the time that the knife couldn't be linked to the murders.
Police Department spokesman Lt. Anthony Alba said at the time that several knives had been found in Simpson's former neighborhood over the past few years but officials did not find any blood or other evidence linking to any crime.
On June 12, 1994, Brown Simpson and Goldman were found stabbed to death at her Los Angeles home. To date, the murder weapon has never been found.
Simpson was charged with the murders. Then on Oct. 3, 1995, the former football star was acquitted of all criminal charges. He was found liable for their deaths in a civil case in 1997.
Simpson was arrested in 2007 during a botched robbery in Las Vegas when he led a group of men into a hotel and casino to steal his own sports memorabilia at gunpoint. He was charged with a number of felony counts, including kidnapping and armed robbery. He was found guilty and sentenced to 33 years in prison. He is serving his time at Lovelock Correctional Facility in Nevada.
Simpson’s lawyer, Malcolm LaVergne, did not immediately respond to a request for comment.