The couple also has a nearly two-year-old daughter, Charlotte.
"We are overjoyed to be grandparents again with the arrival of our grandson, Aidan Clinton Mezvinsky, born on Saturday, June 18, 2016," the former president and first lady said in a statement. "We are all over the moon as Chelsea and Marc welcome Charlotte’s little brother to the world and grateful for our many blessings. Chelsea and Aidan are both doing well and enjoying this very special time together."
Hillary Clinton, who is taking a few days off the campaign trail this weekend, recently hinted that she was on baby-watch.
"I have a fabulous 20-month-old granddaughter. We’re going to have another grandchild sometime early this summer,” she said earlier this month, “And I want to be able to look at them just like I want to be able to look at every one of the children here and every child across this country and say the promise of America is live and well.”
The presumptive Democratic nominee, who says her granddaughter calls her "Grandma," often gushes about being a grandparent.
"It is truly like falling in love all over again. There is nothing like it," she explained at a campaign event in Santa Barbara recently. "It is just the best experience, it’s transformational and until you do it it’s hard to know, and it’s just been for me an absolute life-changing experience."
Chelsea Clinton, who did not reveal the gender of their second child until his birth, announced her second pregnancy in December.