The singer’s wife, Penny Lancaster, gave birth to their second child yesterday, weighing in at 7lb 12oz.
The baby is Stewart’s eighth child.
A statement released on the couple’s behalf said they were “proud and thrilled”.
They already have a son, Alastair, who is five but 39-year-old Lancaster struggled to conceive naturally a second time.
Lancaster underwent IVF and became pregnant on the third cycle.
The statement said: “After the long-awaited arrival of their second child, Rod and Penny are proud and thrilled to welcome Alastair’s baby brother, Aiden, into the world.
“Mother and baby are healthy and blissfully happy.”
The youngster was born in the UK but representatives for the couple would not give any further details.
Lancaster revealed in a magazine interview last year that she was pregnant and talked about the difficulties they had experienced.
Recalling the moment she found out she was expecting, she told Hello! magazine: “I couldn’t believe it. I burst into tears. I called Rod when I was still sobbing.”