The movie will reportedly explore the Washington Post's role in exposing the secret Department of Defense study of U.S. political and military involvement in Vietnam and how the paper's editor, Ben Bradlee, and publisher Kay Graham challenged the federal government over the right to publish the leaked documents in 1971.
Streep, 67, will play Graham, while Hanks, 60, will portray Bradlee.
The announcement of the project is timely in light of President Donald Trump's ongoing battles with the media -- a subject both actors have spoken up about in recent months.
Earlier this year, Streep criticized the president for mocking a disabled reporter during his campaign. When Trump retaliated by calling her "one of the most over-rated actresses in Hollywood," Streep responded with an impassioned speech at the 2017 Human Rights Campaign Greater New York Gala.
"The whip of the executive, through a Twitter feed, can lash and intimidate, punish and humiliate, delegitimize the press and imagined enemies with spasmodic regularity and easily provoked predictability," she said. "We have the right to live our lives, with God or without, as we choose. There is a prohibition against the establishment of a state religion in our Constitution, and we have the right to choose with whom we live, whom we love and who and what gets to interfere with our bodies."
She continued, "As Americans, men, women, people, gay, straight, L,B,G,T,Q, all of us have the human right to life, liberty and the pursuit of happiness. And if you think people got mad when they thought the government was coming after their guns, wait till they come and try to take away our happiness!"
Last week, Hanks gifted the White House Press Corps with an espresso machine. Along with the present was a note encouraging the journalists to "keep up the good fight for Truth, Justice and the American Way. Especially the Truth part."