The singer's wife Penny Lancaster gave birth to their second son Aiden last month in London and he was recently spotted buying baby clothes in department store Harrods.
He said to UK newspaper Daily Express: 'Penny and the baby are doing just fine. Penny's recovering well.
'At my age, a new baby is bloody exhausting, it doesn't stop, but I'm very lucky and proud to have had this happen in my life. Knackered or not, Aiden is a beautiful little boy.'
The baby is the eighth for Stewart as he already has a son Alastair with Lancaster, 39, and six children from previous relationships.