The endorsement is to be released Tuesday, The New York Times reports.
Bush, 29, one of the former president's twin daughters, lives in Manhattan, where she works for the Cooper-Hewitt Design Museum. Her father supported a constitutional amendment that would have banned same-sex marriage.
"I am Barbara Bush, and I am a New Yorker for marriage equality," she says on the video. "New York is about fairness and equality. And everyone should have the right to marry the person that they love."
Meghan McCain, daughter of U.S. Sen. John McCain, R-Ariz., who was the Republican nominee for president in 2008, has also supported gay marriage. Mary Cheney, daughter of former Vice President Dick Cheney, is involved in a long-term lesbian relationship and has been outspoken on the issue, the Times noted.
Celebrity Families of 2014 [PHOTOS]