Mr Trump, 76, faces seven charges including unauthorised retention of classified files, US media reported. The charges are not yet public.
It is the second indictment of Mr Trump and the first ever federal indictment of a former president.
He is campaigning to make a return to the White House in 2024.
Legal experts say the indictment will not limit Mr Trump’s ability to run for the presidency again.
In a post on Truth Social on Thursday, Mr Trump said he was innocent and had been summoned to appear at a federal court in Miami, Florida, on Tuesday afternoon, where he will be arrested and hear the charges against him.
“I never thought it possible that such a thing could happen to a former president of the United States,” he wrote.
He added: “This is indeed a dark day for the United States of America. We are a country in serious and rapid decline, but together we will Make America Great Again!”
Mr Trump’s attorney Jim Trusty told CNN the former president had received details of the charges in a summons document.
He said they include conspiracy, false statements, obstruction of justice, and illegally retaining classified documents under the Espionage Act.
The Department of Justice (DOJ) declined to comment and the indictment has not been publicly released.
An indictment is a document that sets out details of charges against a person, ensuring they have notice of alleged criminal offenses.
The Secret Service will meet Mr Trump’s staff and his security officers to plan his journey to the Miami courthouse.
Special prosecutor Jack Smith has been considering evidence in the documents case since he was appointed to oversee it by Attorney General Merrick Garland in November.
Last year, Mr Trump’s Florida resort Mar-a-Lago was searched and 11,000 documents were seized, including around 100 marked as classified. Some of these were labelled top secret.
There were reports last week that prosecutors had obtained an audio recording of Mr Trump in which he acknowledged keeping a classified document after leaving the White House in January 2021.
It is against US law for federal officials – including a president – to remove or keep classified documents at an unauthorised location.
Legal experts say Mr Trump will still be able to enter the White House race.
“He can be indicted any number of times and it won’t stop his ability to stand for office,” says David Super, a professor at Georgetown University Law Centre.
Mr Super noted that Mr Trump could continue to run for office even if convicted in the documents case.
The property and reality TV mogul is currently the frontrunner among Republican candidates for the White House, according to opinion polls.
As Mr Trump issued a fundraising email with the subject line “BREAKING: INDICTED”, several leading Republicans voiced their support for him.
Speaker of the House of Representatives, Kevin McCarthy, said it was “unconscionable for a president to indict the leading candidate opposing him”.
“House Republicans will hold this brazen weaponisation of power accountable,” he wrote on Twitter.
Mr Trump’s rival for the 2024 nomination, Florida Governor Ron DeSantis said: “We have for years witnessed an uneven application of the law depending upon political affiliation.
“The DeSantis administration will bring accountability to the DOJ, excise political bias and end weaponisation once and for all,” he added.
Vivek Ramaswamy, who is also in the running, said he would “commit to pardon Trump promptly on January 20, 2025, and to restore the rule of law in our country”.
But another candidate, Asa Hutchinson, said Mr Trump’s alleged actions “should not define our nation or the Republican Party”.
A separate probe into efforts to overturn the results of the 2020 election, which Mr Trump lost, is also being overseen by Jack Smith, a former war crimes attorney who is known as a dogged investigator.
Mr Trump became the first former president to be charged with a crime this April, after he pleaded not guilty to 34 counts of falsifying business records over a hush-money payment to a porn star.
He faces a trial in that case in New York next year.