David R. Waters, 52, a former office manager for O'Hair, faces up to 10 years in prison and $250,000 in fines on each count of being a felon in possession of firearm ammunition and possession and interstate transportation of firearms and ammunition by a felon.
U.S. District Judge Sam Sparks will set a sentencing date later.
Convicted of murder in Illinois in 1965, Waters was on probation for skimming $54,000 from the O'Hair family's atheist organizations when police searched his Austin apartment March 25. Police said they found 119 rounds of handgun ammunition.
Waters has not been charged in the O'Hairs' September 1995 disappearance.
But in a 36-page Internal Revenue Service affidavit unsealed Wednesday, authorities said Waters orchestrated a plot to steal at least $600,000 from O'Hair's United Secularists of America.
The document, the first official account of Madalyn Murray O'Hair's disappearance, says motives of money and hatred drove Waters to commit the killings and bury the three in a Texas field.
"Waters ... expressed fantasies of killing Madalyn," the affidavit said. "He spoke about seeing Madalyn suffer and snipping off her toes."
O'Hair vanished from San Antonio with her son, Jon Garth Murray, and granddaughter Robin Murray, and $500,000 in gold coins.
Authorities have theorized the O'Hairs' remains were buried in large barrels, but two searches of a ranch near San Antonio recently failed to find either barrels or bodies.
The newly released court document, an affidavit from IRS special agent Edmund I. Martin, names Waters, along with Gary Karr, now imprisoned in Detroit; Danny Fry, who was killed shortly after the O'Hairs vanished; and Gerald Lee Osborne of Fort Worth.
The affidavit was used in early March to obtain a search warrant of Waters' Austin apartment. The search yielded, among other items, personal correspondence of Jon Murray, the document said.
Martin also stated that Waters was responsible for the death of Fry, whose headless, handless body was dumped in eastern Dallas County on Oct. 2, 1995, two days after the O'Hairs vanished.
Waters used a Ford van rented by Karr to transport the bodies, and Karr told the informant that one of the persons killed was a woman named O'Hair, her daughter and son and another man, the affidavit said.
Authorities have found "what appeared to be blood under the door mat and in a number of places in the van," the affidavit said.
The document added that Waters later in 1995 called Karr and asked him to come back to Texas.
"Waters wanted to rebury the bodies of the O'Hairs because their hands were sticking out of the ground. Karr returned to Texas, but refused to help Waters, so they left the bodies as they were," the affidavit said.
Waters worked for O'Hair in Austin in 1993 and 199and "was open about his dislike of the O'Hairs and made comments about harming Madalyn," the document said, citing an informant.
Written by Katie Fairbank