The couple, who were engaged in 1996, previously starred together in the thriller Seven.
The film also features Meryl Streep playing Martha Mitchell, the wife of Nixon's Chief of Staff John Mitchell.
Paltrow will play Maureen Dean, who stood by her husband John, another member of the Nixon team, as the administration slowly sank into scandal, according to moviehole.net.
"I love Ron Howard's movie. That was about what a nightmare Nixon was to get the rights for the (David) Frost interview and the negotiations back and forth for that.
"But that movie is really about a woman who said our government is corrupt, and 'Why is no on believing me? Why is no one seeing that this Tricky Dicky Nixon is insane?'
"I also think it's the perfect time to make this movie. We'll shoot in the fall and put it out next fall."
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