The park's name derives from two of its abutting streets.   James Madison (1751-1836), was the fourth President of the United States.  He is considered the Father of the Constitution, was an author of the Federalist Papers (along with Alexander Hamilton and John Jay), and helped frame the Billl of Rights.  He was married to Dolley Payne Todd Madison.

 The triangle on which the park is located is named for Mother Francis Xavier Cabrini (1850-1917), a Catholic saint who founded the Missionary Sisters of the Sacred Heart.   Mother Cabrini's remains are buried near a high school named for her, in upper Manhattan on Cabrini Boulevard (formerly Northern Avenue).

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