Applause broke out in the courtroom after the judge's announcement Thursday.
The judge revoked bail after the financier entered 11 guilty pleas.
The judge says the 70-year-old Madoff has the means to flee and an incentive to do so because of his age.
Madoff admitted he began operating a giant Ponzi scheme in the early 1990s. Prosecutors say he robbed investors of billions of dollars.
Sentencing has been set for June 16. He could face up to 150 years in prison.