Sam Bankman-Fried, the disgraced former cryptocurrency executive, was granted release from custody on Thursday by a federal magistrate judge who imposed highly restrictive bail conditions including a $250 million bond and a requirement that he remain in home detention with his parents in California.

The appearance in Federal District Court in Manhattan came just hours after Mr. Bankman-Fried, 30, arrived in the United States following his extradition from the Bahamas, where he was arrested at a luxury apartment complex on Dec. 12 and held in a local jail.

Under the bail arrangement, Mr. Bankman-Fried will live with his parents in Palo Alto, Calif., under strict electronic monitoring, including a bracelet that will be placed on him before he leaves the courthouse.

The $250 million personal recognizance bond — a written promise to appear in court as needed — will be secured by his parents’ interest in their home, the judge said. He was also required to surrender his passport and to receive mental health and substance abuse treatment. Any expenses above $1,000 would require prior approval by the government.

The judge, Gabriel W. Gorenstein, warned Mr. Bankman-Fried that if he failed to appear in court or violated any of the other conditions, a warrant would be issued for his arrest and he and his parents would be responsible for paying the hefty bond.

Asked whether he understood, Mr. Bankman-Fried responded, “Yes, I do,” the only words he uttered in the hearing, which lasted less than an hour.

Discussions about a bail deal had begun even before Mr. Bankman-Fried was extradited. In court on Thursday, the deal was formally proposed by the U.S. prosecutors in the Southern District of New York who brought the charges against Mr. Bankman-Fried.

Mr. Bankman-Fried was escorted into court wearing a dark suit and was seated between his two lawyers, Mark Cohen and Christian Everdell.

Mr. Cohen argued that Mr. Bankman-Fried was not a flight risk. “My client voluntarily consented to come to face these charges here in New York,” he told the judge. “He wants to address them.”

Nicolas Roos, an assistant U.S. attorney, said Mr. Bankman-Fried had committed crimes of “epic proportions” and that the case against him involved multiple cooperating witnesses, as well as encrypted text messages and tens of thousands of pages of financial records. But he noted that Mr. Bankman-Fried had “family and communities ties” and that his wealth had “diminished significantly.”

“It would be very difficult for this defendant to hide without being recognized,” Judge Gorenstein said. “So I believe that the risk of flight is appropriately mitigated.”

Mr. Bankman-Fried has been charged with two counts of wire fraud and six counts of conspiracy related to securities and commodities fraud, money laundering and violating the campaign finance laws.