The public version of the affidavit, a court document that includes evidence presented by prosecutors, could reveal new details about the inquiry.
The Department of Justice opposed releasing an unredacted version amid its ongoing investigation.
The FBI search was part of a probe into the potential mishandling of documents.
Trump has denied wrongdoing and insists the classified files that investigators say were found at Mar-a-Lago in Palm Beach had already been declassified by himself.
On Thursday, US Magistrate Judge Bruce Reinhart ordered the affidavit to be released with redactions by noon on Friday (4am Saturday NZT).
He said prosecutors had demonstrated a “compelling reason” to black out parts of the document, which would reveal the identities of witnesses, law enforcement agents and uncharged parties, as well as “the investigation’s strategy, direction, scope, sources and methods”.
His ruling came shortly after the justice department confirmed that it had submitted to the judge a copy of the affidavit with proposed redactions.
Even in redacted form, the affidavit could provide clues as to why Trump allegedly took classified documents with him in the chaotic final days of his presidency and what he did with them while they were stored in Palm Beach.
The rest may have to wait for when – or if – any criminal charges are filed.
The warrant itself was released on 12 August alongside an inventory of recovered items that showed 11 sets of classified files were removed from the estate.
Several news organisations have applied for the affidavit to be unsealed, citing public interest given the historic nature of the search of a former president’s home.
The Department of Justice, however, had resisted the move, arguing that its release could cause “irreparable damage” to its ongoing investigation. It also said the necessary redactions would render the document “meaningless”.
Trump and his lawyers – who characterised the Mar-a-Lago search as politically motivated and unlawful – called for the unredacted affidavit to be released.
A spokesperson for Trump, Taylor Budowich, said that efforts to “hide” its contents were “cynical” and could be used to “hide government corruption”.
Earlier this week, Trump’s legal team asked that the investigation be frozen and that an independent third-party attorney, known as a special master, be brought in to oversee the documents that the FBI took during the search.
The search warrant indicates FBI agents wanted to see if Trump committed a crime by improperly handling government records when he took them from the White House to Mar-a-Lago as his administration ended.
US presidents are required to transfer documents and emails to the National Archives when they leave office.