Davis will essay Chisholm, who was also the first woman and person of colour to pursue a nomination for president in a major American political party.
The actor said she hope to "educate" because a lot of people "don't know who she was".
"Everyone can be brave and bold if you have it in you," she told The Hollywood Reporter.
Davis will also produce the feature with husband Julius Tennon as the first of a series of politically-themed films the couple makes for the streaming giant.
"We want do the same thing - make content that highlights people of colour across the globe," Tennon said of the deal with Amazon.
The movie is yet to be titled.
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