Chelsea, 34, made the announcement at a public event with her mother in New York organised by a Clinton Foundation initiative to advance the cause of women and girls around the world.
"Marc and I are very excited that we have our first child arriving later this year," Chelsea told the audience at the Lower Eastside Girls Club, to whoops of delight from the crowd.
"And I certainly feel all the better -- whether it's a girl or a boy -- that she or he will grow up in a world full of so many strong female leaders," she added.
"Thank you for all of the kind words!" she wrote, after a deluge of messages congratulating her.
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Former US president Bill and former US secretary of state Hillary could hardly contain themselves.
"Excited to add a new line to my Twitter bio... grandfather-to-be! @HillaryClinton and I are so happy for Chelsea and Marc!," tweeted Bill.
"My most exciting title yet: Grandmother-To-Be! @billclinton and I are thrilled that Chelsea and Marc are expecting their first child!" tweeted Hillary five minutes later.
Jenna Bush Hager, whose father George W Bush was elected in 2000 to replace Bill Clinton as US president, tweeted her congratulations and "welcome to the best club in the world."
Chelsea, who works full time with the Clinton Foundation, married long-term boyfriend Marc Mezvinsky in 2010 and the couple live in Manhattan.
Their news had been widely anticipated. Beside Hillary Clinton's impatience for a grandchild, Chelsea recently told Glamour magazine of the couple's eagerness to start a family.
A foray into television journalism and frequent appearances on conference stages have rapidly increased Chelsea's prominence as a young woman widely tipped to enter politics herself one day.