Madoff, 82, died at the Federal Medical Center in Butner, North Carolina, the bureau said in a statement.
His death was announced by the Bureau of Prisons.
The bureau said Madoff’s cause of death would be determined by a medical examiner.
Mr Madoff had been serving a 150-year sentence after he pleaded guilty in 2009 to running a Ponzi scheme, which paid investors with money from new clients rather than actual profits.
It collapsed during the 2008 financial crisis.
Last year, Madoff’s lawyers filed court papers to try to get him released from prison in the COVID-19 pandemic, saying he had suffered from end-stage renal disease and other chronic medical conditions. The request was denied.
“Bernie, up until his death, lived with guilt and remorse for his crimes,” his lawyer Brandon Sample said in a statement.
“Although the crimes Bernie was convicted of have come to define who he was – he was also a father and a husband. He was soft spoken and an intellectual. Bernie was by no means perfect. But no man is.”
Mr Madoff, the son of European immigrants who grew up in New York, set up his eponymous firm Bernard L Madoff Investment Securities in 1960.
The company became one of the largest market-makers – matching buyers and sellers of stocks – and Mr Madoff served as chairman of the Nasdaq stock exchange.
The firm was investigated eight times by the US Securities and Exchange Commission because it made exceptional returns.
But it was the global recession which effectively prompted Mr Madoff’s demise as investors, hit by the downturn, tried to withdraw about $7bn from his funds and he could not find the money to cover it.
For decades, Madoff enjoyed an image as a self-made financial guru whose Midas touch defied market fluctuations. A former chairman of the Nasdaq stock market, he attracted a devoted legion of investment clients — from Florida retirees to celebrities such as famed film director Steven Spielberg, actor Kevin Bacon and Hall of Fame pitcher Sandy Koufax.
Madoff pleaded guilty in March 2009 to securities fraud and other charges, saying he was “deeply sorry and ashamed.”