Brooks, who was editor of the News of the World when the voicemails of murdered schoolgirl Milly Dowler were allegedly intercepted, is to appear before the inquiry on May 11.
Coulson, her successor at the paper, will give evidence a day earlier, along with Daily Mail proprietor Lord Rothermere.
Both Brooks and Coulson have previously appeared in front of a Parliamentary committee on phone hacking, but have never given evidence to Lord Justice Leveson.
Their appearance is expected to provide some uncomfortable moments for Cameron, who has been accused of being too close to Rupert Murdoch and his current and former executives, such as Coulson and Brooks.
Brooks has successfully applied for "core participant" status in the inquiry, meaning she can put questions to other witnesses through her lawyers.
It is expected that she will disclose emails and text messages between herself and Cameron. The Daily Telegraph clams that there could have been as many as a dozen messages a day between the two at one stage.
She was first arrested in July 2011 over allegations of phone hacking and illegal payments to police, and then rearrested this spring on suspicion of conspiracy to pervert the course of justice.
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This will also mark the first time that Coulson has spoken publicly since he was arrested in July 2011 by police investigating allegations of hacking and corruption.
Coulson was appointed Conservative director of communications in May 2007, but quit in early 2011, claiming that the torrent of allegations about hacking made his position untenable.
Both Brook and Coulson deny knowledge of, and involvement in, any illegal activity.
Meanwhile, a 57-year-old ex police officer was today arrested in the Operation Elveden police probe into corrupt payments to officials by journalists.