Jones, a triple gold medalist in Sydney, said she took "the clear" for two years, beginning in 1999, and that she got it from former coach Trevor Graham, the newspaper reported. Graham told her it was flaxseed oil.
"The clear" is a performance-enhancing drug linked to BALCO, the lab at the center of a federal steroids investigation. Until now, Jones had steadfastly denied she ever took any kind of performance-enhancing drugs.
Jones also said she will plead guilty Friday in New York to two counts of lying to federal agents about her drug use and an unrelated financial matter, the Post reported.
"I want to apologize for all of this," the newspaper reported, quoting a person who received a copy of Jones' letter and read it to the paper. "I am sorry for disappointing you all in so many ways."
No one answered the door at Jones' Austin, Texas, home Thursday evening.
The admission could cost Jones the five medals she won at the Sydney Olympics. Though she fell short of her goal of winning five gold medals, she came away with three and two bronzes and was one of the games' biggest stars.
But her career has been tarnished by doping allegations since then. Victor Conte, head of the Bay Area Laboratory Co-Operative, repeatedly has accused Jones of doping.
Jones was one of several athletes to testify in 2003 before a San Francisco federal grand jury that's investigating BALCO, and former boyfriend Tim Montgomery was given a two-year ban for doping in late 2005.
In December 2004, the International Olympic Committee opened an investigation into doping allegations against Jones.
Last year, a Jones urine sample tested positive for the performance-enhancing drug EPO. Jones immediately quit a European track tour and returned to the United States. Although she was cleared when a backup sample tested negative, she missed at least five major international meets, forfeiting an estimated $300,000 in appearance and performance fees.
In her letter, Jones said she'd used performance-enhancing drugs until she stopped training with Graham at the end of 2002. She said she lied when federal agents questioned her in 2003, panicking when they presented her with a sample of "the clear," which she recognized as the substance Graham had given her.
"Red flags should have been raised when he told me not to tell anyone," the Post reported, quoting the letter.
Graham was indicted in the BALCO case last November on three counts of lying to federal agents. He has pleaded not guilty, and a trial is set for Nov. 26,
A woman who answered the phone at Graham's home in Raleigh, N.C., declined to identify herself, but said Graham was not home before refusing to answer any other questions. There was no answer at the door of Graham's north Raleigh home on Thursday.
The Post also reported that in her letter, Jones said she lied about a $25,000 check given to her by Montgomery, who pleaded guilty in New York this year as part of a multimillion-dollar bank fraud and money-laundering scheme. Jones' former agent, Charles Wells, and coach, Steven Riddick, were also part of the scheme.
Documents filed in a federal court in Manhattan show that Jones received the check from a Virginia man who prosecutors have accused of enlisting friends and business partners to help launder the proceeds of the multimillion-dollar plot.
The money was drawn on an account established with one of $5 million worth of stolen, forged or doctored checks that investigators said the conspiracy attempted to cash over three years.
Though Jones told investigators she knew nothing about the check, the Post reported that she said in her letter that Montgomery told her it was from the 2005 sale of a refurbished vehicle and was partial payment for $50,000 she had loaned him.
"Once again, I panicked," the Post reported. "I did not want my name associated with this mess. I wanted to stay as far away as possible."
In her prime, Jones was one of track's first female millionaires, typically earning between $70,000 and $80,000 a race, plus at least another $1 million from race bonuses and endorsement deals.
In 2000-01, she competed in 21 international events, including the Sydney Olympics, where she won five medals - three gold.