NEW YORK - Many of Bernard L. Madoff's victims who thought they lost everything could get at least half their money back after the widow of a Florida philanthropist agreed Friday to return a staggering $7.2 billion that her husband reaped from Madoff's giant Ponzi scheme.

Federal prosecutors reached the settlement with the estate of Jeffry Picower, a businessman who drowned after suffering a heart attack in the swimming pool of his Palm Beach, Fla., mansion in October 2009. Picower was the single biggest beneficiary of Madoff's fraud.

U.S. Attorney Preet Bharara called the forfeiture the largest in Justice Department history and a "game changer" for those swindled by Madoff.

He commended Picower's widow, Barbara, "for agreeing to turn over this truly staggering sum, which really was always other people's money."

The amount greatly expands the $2.3 billion sum that Irving H. Picard, the court-appointed trustee trying to recover money for the victims, had collected through asset sales and other settlements in the Madoff bankruptcy. The $7.2 billion figure represents the difference between the cash that Picower put into his Madoff account and the amount that he withdrew over the life of the fraud, according to litigation filed last year by Picard.

"We will return every penny received from almost 35 years of investing with Bernard Madoff," Barbara Picower said in a statement. "I believe the Madoff Ponzi scheme was deplorable, and I am deeply saddened by the tragic impact it continues to have on the lives of its victims. It is my hope that this settlement will ease that suffering."

The settlement means roughly half of the $20 billion that investors entrusted to Madoff has now been recovered, authorities said.

Madoff, 72, is serving a 150-year prison sentence for defrauding his investors.

His burned clients greeted Friday's news warily.

Willard Foxton, a British journalist whose father committed suicide after losing his life savings, said he was stunned that a major investor decided to return so much money.

"I don't think he would have killed himself if he thought a few years down the line that he was going to be getting a good amount of his money back," he said.

Foxton added: "I thought we had zero chance of getting any money back, and I still am very, very skeptical. If I see a penny before 2015, I'd be amazed."

Lawrence Velvel, a law school dean who lost money he had invested with Madoff for decades, said Picower's widow "did the right thing."

But he was wary about who, in the end, would benefit more - the multitude of small and mid-sized investors who had been counting on their investments for their retirement, or the big hedge funds that did business with Madoff.

"It's going to go to the hedge funds," he said.

Jeffry Picower, who was 67 when he died, was one of Madoff's oldest clients. The bogus profits, or more than a third of the overall sum that disappeared in the scandal, was supposedly made on stock trades. But authorities said it was simply stolen from other investors.

Picower's lawyers said he knew nothing about the scheme, but Picard, the trustee, had argued in court papers that the businessman must have known the returns were "implausibly high" and based on fraud.

Barbara Picower said she was "absolutely confident that my husband, Jeffry, was in no way complicit in Madoff's fraud and want to underscore the fact that neither the trustee, nor the U.S. attorney, has charged him with any illegal act."

A huge charitable foundation that Picower had created closed in 2009 after its assets were wiped out in the Madoff fraud. It had donated hundreds of millions to colleges, libraries, and other groups.

Thousands of people, banks, and hedge funds that invested with Madoff saw their savings wiped out when the fraud was revealed in December 2008. Many, though, like Picower, had been drawing bogus profits from their Madoff accounts for years and walked away from the scheme having taken out more money than they put in.

Madoff's clients had thought, based on his fraudulent account statements, that they had more than $60 billion invested in stocks with Madoff.

Investigators found, though, that no investments were made, and that an estimated $20 billion in principal was simply being paid out bit by bit to other investors.

The New York Times News Service contributed to this article.