The 66-year-old rock star and his wife said they were "proud and thrilled" to announce the "long awaited arrival.” Aiden joins big brother Alastair, who is five years old.
Lancaster and Stewart, who have been together for more than a decade, revealed they were expecting last summer after intensive IVF treatment.
"I couldn’t believe it. I burst into tears. I called Rod when I was still sobbing," Lancaster said.