UPDATE 2: NPR's Justice Department correspondent:
However, Politico reports the White House may be handling this matter without DOJ or FBI assistance:
Neither DOJ nor the FBI has any idea how the redaction process for this announcement is being handled, and they think it’s possible that the White House is just doing it on its own and could release this material as early as Monday night, according to a source familiar with the process.
(...)
Legal experts said some of the actions Trump ordered had the potential to violate the Privacy Act, a federal law protecting against disclosure of personal information in government files.
“There could very likely be Privacy Act implications,” former Justice Department attorney Scott Hodes said.
However, Hodes said officials might be able to work around those legal obstacles by turning over the records to Congress, which could make them public. “If they have a legitimate reason to give them to Congress, Congress is not covered by the law, so it’s not a Privacy Act violation.”
(...)
“Trump has ordered the release of sensitive information into an ongoing investigation of himself and his friends--information that his own Justice Department did not want released because it would jeopardize ongoing investigations,” said former federal prosecutor Renato Mariotti. “That is corrupt, plain and simple.”
Trump orders declassification of surveillance application, release of Comey texts (Politico)
UPDATE: Rep. Adam Schiff (D-CA), top Democrat on the House Intelligence Committee, responds:
President Trump, operating separately from his own Justice Department but in lockstep with congressional allies eager to discredit the Russia investigation, is ordering the DOJ to declassify "20 pages of the surveillance application that authorized the FBI to monitor [his own former] campaign adviser Carter Page."
The move, long foreshadowed by calls from Trump's top allies in Congress, also includes an effort to reveal the details of former Justice Department official Bruce Ohr's interviews connected to the Russia investigation.
Trump also directed the Justice Department to publicly release all text messages "relating to the Russia investigation, without redaction" of Ohr, former FBI Director James Comey, former Deputy Director Andrew McCabe and former FBI officials Peter Strzok and Lisa Page.
Trump made the extraordinary move in response to calls from his allies in Congress who say they believe the Russia investigation was tainted by anti-Trump bias within the ranks of the FBI and Justice Department. It also came as Trump continued his efforts to undermine special counsel Robert Mueller’s probe in the wake of the guilty plea of his former campaign chairman, Paul Manafort, and amid the ongoing grand jury investigation into a longtime associate, Roger Stone.
Trump’s decision will result in the release of text messages and documents involving several top Justice Department and FBI officials who Trump has repeatedly attacked over the last year.
The White House's official statement:
Trump orders declassification of surveillance application, release of Comey texts (Politico)
Trump declassifies documents related to FBI Russia probe (AP)