Alexander, professor of African-American studies at Yale University, was chosen by President-elect Barack Obama to compose and read a poem for his inauguration on Jan. 20.
"I'm completely thrilled and deeply, deeply honored," Alexander said Thursday.
Alexander's mother is a historian specializing in African-American women's history at George Washington University. Her father was a presidential civil rights adviser and secretary of the Army.
"The civil rights movement was fully alive in our home," Alexander said.
Attending King's 1963 speech was an iconic moment for the family.
"That story was always a part of family stories that were told as a way of thinking about the importance of being civic, the importance of looking forward, the importance of having visionary leaders, the importance of involving yourself with the community, the importance of recognizing the historical moment and historical possibilities," Alexander said.
Alexander said her parents are thrilled at her selection.
"This is an incomparable thrill to them in the way that Obama's presidency is an especially potent and powerful thing for African-Americans in their 70s who have devoted their lives to progress," Alexander said. "To be a part of it, I almost can't imagine it myself."
Alexander, who is 46 and married with two children, was a Pulitzer Prize finalist in 2005 for her collection "American Sublime." Her other books include "The Venus Hottentot," "Body of Life" and "Antebellum Dream Book."
Last year, she won the $50,000 Jackson Poetry Prize.
Alexander will be only the fourth poet to read at a presidential swearing in. Robert Frost read for President John F. Kennedy, while Maya Angelou and Miller Williams read at President Clinton's inaugurations.
"I think what I hope to symbolize and demonstrate is the important role that arts and literature can play in this moment when the country is thinking so keenly about moving forward and coming together," Alexander said.
Alexander acknowledged the challenge before her. She said she does not start with a message in mind, likening the process to a radio antenna in which she listens for the right language.