The former US president and former secretary of state said they were 'blessed, grateful, and so happy' to become grandparents after Chelsea, gave birth on Friday night.
Chelsea announced the news on Twitter early on Saturday, saying she and husband Marc Mezvinsky were 'full of love, awe and gratitude as we celebrate the birth of our daughter, Charlotte Clinton Mezvinsky'.
The proud grandparents said in a statement: "Chelsea is well and glowing. Marc is bursting with pride. Charlotte's life is off to a good start."
Chelsea later tweeted:
At 7:03 PM on September 26th, we finally met Charlotte. We're in love. pic.twitter.com/9ZCkoa6BPU
- Chelsea Clinton (@ChelseaClinton) September 27, 2014
The Mezvinskys live in New York City, but the family did not say where the child was born or provide additional details on her birth.
The news comes as Hillary Clinton decides whether to run for the White House in 2016.
She is the leading Democratic contender to succeed President Barack Obama, her 2008 campaign rival, and has said she expects to make a decision around the beginning of next year.
The baby has been eagerly anticipated, with the former first lady and senator for New York calling grandmother her 'most exciting title yet'.
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She has even picked out the first book she intends to read to her grandchild, the classic Goodnight Moon.
Bill cancelled a Saturday fundraising visit to Denver, saying: "I hope I get an excused absence. You all know my family just got a little bigger, and I figured I should stay home where I'm really needed."
Chelsea announced her pregnancy in April, at the end of a forum in New York on female empowerment.
She said at the time: "I just hope I will be as good a mom to my child and, hopefully, children as my mom was to me."