Evidently delighted, Rod - now a father for the eighth time at the age of 66 - said: "Aiden is our miracle baby," referring to the fertility problems the couple encountered.
Penny endured two gruelling rounds of IVF before a successful third cycle gave the pair everything they had wished for.
The former model was moved to tears as she spoke of her happiness.
"Aiden is the best birthday present I could have wished for. My family is now complete," said Penny, referring to his grand debut the day after her 40th.
Far from the new arrival putting a strain on their marriage, the couple insisted having another child has strengthened their bond.
"Parenthood has taken our relationship to a new love and understanding," said Rod.
Whereas many new mums attempt to bounce back into shape as quickly as possible, Penny is planning on taking it easy for a while.
"I’d like to get rid of the excess weight eventually, but the doctors advised not to start exercising for six weeks," she explained.
"I didn’t try for all those years to fall pregnant just to be vain about it".
Pick up your copy of this week's HELLO!, issue 1168, for the full story, plus an exclusive interview with Cheryl Cole on the royal wedding.
Rod and Penny: How an unknown photographer and a rock legend clicked
It's a little princess!