"The vice president took me aside and gave me the good news," Bush told People magazine. "He and his wife, Lynne, are very happy for Mary."
In 2005, Bush said he believed a child should be "raised in a married family with a man and a woman."
Asked if he still felt that way, knowing Mary and her partner, he said, "I think Mary is going to be a loving soul to her child. And I'm happy for her."
Mary Cheney, 37, and Poe, 45, have been together for 15 years and are expecting their first child late in the spring.
Although Cheney was a key aide on her father's 2004 re-election campaign, she has said she disagrees with Bush's stance on gay marriage.
"I am in favor of legalized same-sex marriage," she told People in May.
But during the campaign, she said, "I had no doubt, even with that disagreement, that President Bush was the absolute best person to be leading us at this time in our country's history," she says.