The 34-year-old, whose husband is investment banker Marc Mezvinsky, tweeted the news to her 624,000 followers shortly after midnight tonight - four days before the expected due date.
She said: 'Marc and I are full of love, awe and gratitude as we celebrate the birth of our daughter, Charlotte Clinton Mezvinsky.'
The baby is the first grandchild of Bill and Hillary Clinton, who have gushed at length about their excitement at a number of public speaking events in the past few months, and both retweeted their daughter's post tonight.
Chelsea was last seen on Wednesday afternoon at the annual Clinton Global Initiative summit in New York's Sheraton Hotel, where she had been on her feet for three days straight.
Despite resigning from her position as a specialist reporter for NBC in April, the former First Daughter, who was educated at Stanford, Oxford and Columbia universities, continued to work full-time for the Clinton Foundation up until she gave birth.
News of the birth - four days before the expected due date - will come as welcome news to supporters of Hillary Clinton running for president since the former First Lady said she would wait until she became a grandmother before launching a second bid for the nomination.
A spokesman for the new parents, Kamyl Bazbaz, confirmed Clinton had the child on Friday.
On Tuesday, Chelsea appeared on cnn with her growing baby bump as she revealed they had decided not to find out the gender of their first child until the birth as they wanted it to be a surprise.
'There are so few mysteries in life...any answer is a happy one,' Clinton told cnn's Fareed Zakaria on Tuesday.
'So my husband and I decided that we would enjoy this mystery for the nine-plus months that we're granted, and we are eager to find out what God will have given us.'
The name Charlotte dates back to the 1700s, and means 'freedom'.
It has long been a favourite among royals and political dynasties, and last year it was the 11th most popular girl names in the United States.