The Democrat said in a statement he believes people of the 13th Congressional District "are searching for leadership with bold, new ideas in Washington, D.C."
Espaillat represents Washington Heights. He was elected to the Assembly in 1996, and became a state senator in 2010.
If he beats Rangel, he would become the first Dominican American to be elected to Congress.
The district's lines have been redrawn under new congressional redistricting. The new district includes most of Harlem, Washington Heights and part of the Bronx.
Rangel campaign said the 81-year-old congressman was committed to running for a 22nd term.
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