"Marc and I are full of love, awe and gratitude as we celebrate the birth of our daughter, Charlotte Clinton Mezvinsky," Clinton said in the post on her Twitter and Facebook profiles, referring to her investment banker husband Marc Mezvinsky.
Details on the baby's height and weight have not been released.
Charlotte's new grandparents shared their excitement about the birth in a joint statement.
"We are thrilled to be with our daughter and her husband as they welcome their daughter into the world," the senior Clintons said.
"Chelsea is well and glowing. Marc is bursting with pride. Charlotte's life is off to a good start," they said.
Chelsea Clinton announced her pregnancy in April while sitting side-by-side with her mother in armchairs on a stage at a New York City event on empowering women.
It remains unclear how the birth of the first Clinton grandchild will affect the political ambitions of Hillary Clinton, who is considering a run for the White House in 2016.
In 2011, former president Clinton told reporters in Davos, Switzerland: "I would like to have a happy wife, and she won't be unless she's a grandmother ... It's something she wants more than she wanted to be president."