"At 7:41 AM Saturday, our family and hearts expanded with Aidan's arrival," she captioned the photo shared on Twitter. "We are blessed."
The former secretary of state captioned the photo, "What a joy being with our new grandson, Aidan. So grateful. -H."
And in his own words, former president Bill Clinton shared his own sentiments about becoming a grandad again.
"Aidan has made two dads very happy this Father's Day," he tweeted along with a photo of himself caressing Aidan's head while Mezvinsky, 38, holds him. "Hillary and I are thrilled for Marc and Chelsea!"
Chelsea Clinton and Mezvinsky, who wed in 2010, are already parents to a nearly 2-year-old daughter, Charlotte.