A representative for the pair 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.
"Born February 16th 2011, weighing 7lb12oz, mother and baby are healthy and blissfully happy."
The new arrival is a much-longed-for little brother for the couple's five-year-old.
Penny and Rod broke originally broke the news on hellomagazine.com back in August 2010 that they were expecting.
A month later, the 39-year-old model and her rocker husband opened up to HELLO! magazine about the emotional struggle they had to fulfil their dream of having another child.
The couple went through three grueling rounds of IVF before 39-year-old Penny finally became pregnant.
Of the day she found out, she remembers: "I couldn’t believe it. I burst into tears. I called Rod when I was still sobbing.
"Rod said, 'I’m in the middle of a restaurant in Russia, crying.' I kept pinching myself. Neither of us could believe it."
The couple have been together for over ten years, getting together after Rod invited Penny to take some pictures of him at a concert.