UsMagazine.com said Stewart's wife, Penny Lancaster, gave birth to their son, Aiden, Wednesday.
"Rod and Penny are thrilled... Mother and baby are healthy and blissfully happy," the representative told the magazine's Web site Thursday.
The baby weighed in at 7 pounds, 12 ounces.
Stewart, 66, and Lancaster, 39, have been married since 2007. They also have a 5-year-old son named Alastair.
The recording star has six children from previous relationships ranging in age from 16 to 31. A seventh child born in 1964 was given up for adoption, UsMagazine.com said.