The Tower Heist star will also direct and executive produce the project, from Extremely Loud and Incredibly Close novelist Jonathan Safran Foer, according to Deadline.
Alan Alda - whose last regular television role was on NBC's The West Wing - is in negotiations to appear alongside Stiller.
"Ben Stiller continues to be a major, multi-talented star because of his discerning ability to embrace creative and innovative projects – whatever the medium," said HBO's president of programming Michael Lombardo.
"We were enormously pleased that Ben responded to this extraordinary work from Jonathan Safran Foer."
Described as "politically, religiously, culturally, intellectually and sexually irreverent", All Talk follows the dramatic personal lives of a Jewish family in Washington, DC.
The Girl with the Dragon Tattoo's Scott Rudin will executive produce alongside Stiller, Foer and Eli Bush.
Filming on All Talk is expected to begin in mid-2012.
Stiller - who first rose to fame on Fox's The Ben Stiller Show - will next direct, produce and star in comedy remake The Secret Life of Walter Mitty.
> Aaron Sorkin The Newsroom taken to series by HBO
> Ewan McGregor to star in HBO's The Corrections pilot