The singer, 62, and husband David Furnish, 48, welcomed son Zachary Jackson Levon Furnish-John on Dec. 25, John's rep confirms to PEOPLE.
The 7 lb., 15 oz., baby was delivered via surrogate in California.
"We are overwhelmed with happiness and joy at this very special moment," the couple, who exchanged vows in a civil ceremony in 2005, said in a statement. "Zachary is healthy and doing really well, and we are very proud and happy parents."
Just last year, Furish told PEOPLE they were going to wait to start a family until John was ready to come off the road.
"We don't want to put the raising of children into the hands of nannies and housekeepers," said Furnish. "We want to be active parents. We have godchildren [and] kids that we support in Africa, so we're fine."