Madoff had been under house arrest in his $7m Manhattan apartment as part of his $10m bail, which has also required his assets to be frozen.
Speaking in court after pleading guilty, Madoff said he was "grateful for this opportunity to publicly comment about my crimes, for which I am deeply sorry and ashamed".
Madoff is accused of soliciting billions of dollars from pension funds, charities and other investors in a scheme that prosecutors say began in the 1980s.
He told the judge presiding over the US district court in New York that he began the fraud expecting it to be short.
"As the years went by, I realised my risk, and [that] this day would inevitably come. I cannot adequately express how sorry I am for my crimes," he said.
No plea deal
Madoff was charged with one count of securities fraud following his arrest in December, but US authorities revealed 10 additional charges against him earlier in the week.
The 70-year-old confessed to investigators that he ran the scheme - in which early investors are paid off with the money of newer clients - over many years with losses of as much as $65bn.
Al Jazeera's John Terrett, reporting outside the courthouse in New York, said Madoff was accused with "quite literally masterminding the biggest swindle in US financial history".
Brad Freedman, a lawyer representing about 100 of the alleged victims, said that while some of those who lost their investments to Madoff were celebrities or "super wealthy", most were not.
"Most of the victims are people who worked their entire lives ... put their life-savings with Mr Madoff, and lost the entirety of it," Freedman told Al Jazeera.
Judge Chin said that the victims of the alleged fraud will be heard in court before sentencing.