Former President Bill Clinton and former Secretary of State Hillary Rodham Clinton finally have the titles they have long wanted: Grandpa and Grandma.

Their daughter, Chelsea, gave birth to her first child — with her husband, Marc Mezvinsky — on Friday and posted the news on Twitter early Saturday. “Marc and I are full of love, awe and gratitude as we celebrate the birth of our daughter, Charlotte Clinton Mezvinsky,” Ms. Clinton said.

Mr. Clinton, in a statement on Saturday afternoon, said that “Charlotte’s life is off to a good start.”

“Chelsea is well and glowing,” he said. “Marc is bursting with pride.”

As late as Wednesday afternoon, Ms. Clinton was on stage delivering speeches and moderating panels at the Clinton Global Initiative gathering in New York.