Doan Cleare, The Bahamas' acting commissioner of Corrections, told Reuters the documents were signed about noon on Tuesday.
A hearing in Bankman-Fried's case will take place on Wednesday at 11am, a court official told Reuters.
Wednesday's proceeding could set the stage for the 30-year-old cryptocurrency mogul to depart the Caribbean country after several days of confusion about the status of Bankman-Fried's extradition.
A US-based lawyer for Bankman-Fried did not respond to requests for comment.
A person familiar with the matter said Bankman-Fried intends to consent to extradition.
Bankman-Fried has acknowledged risk-management failures at FTX but has said he does not believe he has criminal liability.
A spokesman for the US attorney's office in Manhattan declined to comment.
Bankman-Fried was arrested last week in The Bahamas, where he lives and where FTX was based, after a grand jury sitting in Manhattan federal court indicted him for allegedly stealing customer funds to plug losses at Alameda Research, his crypto hedge fund.
He initially told a Bahamas court he would contest extradition but Reuters and other outlets reported over the weekend that he would reverse his decision.
During a court hearing on Monday at which Bankman-Fried appeared, his local defence lawyer Jerone Roberts said he had not been informed of the purpose of the proceeding.
He later said that while his client had seen an affidavit laying out the charges against him, he wanted to access the complete indictment before agreeing to extradition.
Earlier on Tuesday, Roberts declined to comment as he departed Magistrate Court in the capital Nassau.
US embassy officials earlier entered the courthouse, a Reuters witness said, but Bankman-Fried was not seen on Tuesday.
The arrest capped a stunning fall from grace for Bankman-Fried, who rode a boom in the values of bitcoin and other digital assets to become a billionaire several times over.
He has been under increasing scrutiny since early November, when customers raced to withdraw funds from FTX amid concerns over commingling of their assets with Alameda.
Damian Williams, the top federal prosecutor in New York City, said last week that Bankman-Fried's actions amounted to "one of the biggest financial frauds in American history."
The $US32 billion ($A48 billion) exchange declared bankruptcy on November 11 and Bankman-Fried stepped down as CEO on the same day.
He has since been detained at The Bahamas Department of Corrections in Nassau, formerly known as Fox Hill prison.
The US State Department in a 2021 report described conditions at the facility as "harsh," citing overcrowding, rodent infestation and prisoners relying on buckets as toilets.
Local authorities say conditions have since improved.
