The book's title comes from an interview Woodward conducted with Trump in April 2016 in which he said he believes power is derived from fear.
CNN reported that Woodward, who is renowned for his work on the Watergate investigation, has been working on the project for the last eight months.
"Fear is the most intimate portrait of a sitting president ever published during a president's first years in office", one source said, adding that the book will take readers behind the scenes of the Trump White House with extensive in-the-room accounts of meetings with the President.
The book, "Fear: Trump in the White House", is set to be released on September 11, according to the book's Amazon.com pre-order page.
Former government officials have spoken out over a new book taking aim at the Trump Presidency - calling it a "killer".
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It's a great opportunity for him to start doing that now. "Absurd? Yes", he wrote in the Daily Telegraph newspaper. The England and Wales Cricket Board confirmed that off-spinner Moeen Ali had been left out from a 13-man squad.
Woodward, famed for his coverage of the Watergate scandal that led to President Richard Nixon's resignation, has written or co-authored 18 books including penetrating looks at George W. Bush and Barack Obama's presidencies.
"The expected tenor of the book is underscored by its unsettling cover, an extreme close-up of a squinty-eyed Trump depicted through a gauzy red filter", Roig-Franzia wrote.
According to the report, Woodward returns his traditional methods in the book to on-the-ground reporting to fill in the details behind the walls of the White House.
The Post also noted that Woodward has been showing up "at important people's houses unannounced to ask for interviews" late at night and has told friends that reporting on Trump has felt like a "rebirth".
"Real power is through respect... real power is, I don't even want to use the word, 'fear, '" Trump reportedly told Woodward and Costa during the interview.