Chelsea Clinton has given birth to a girl, she said in a statement on her Twitter and Facebook profiles, giving former President Bill Clinton and former Secretary of State Hillary Clinton their first grandchild.

"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, referring to her investment banker husband Marc Mezvinsky.

The messages, which came out after midnight on the east coast, were later retweeted by both of the new grandparents.

Chelsea Clinton announced her pregnancy in April while sitting with her mother in side-by-side 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.

Former president Clinton told reporters in Davos, Switzerland, in 2011: "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."