|Thomas Cohen and Peaches Geldof|
Peaches tweeted: "yes, it's true - I'M A MUMMY!
"My little boy is the most beautiful thing in this world. When he holds @tomfromscum's finger with his hand its the sweetest thing ever. (sic)"
Tom added: "I'm a dad he is the most perfect thing ever so proud of his beautiful mum @peaches_g and overcome with joy x (sic)"
Peaches' publicist later confirmed the news, but didn't say when the baby had been born.
He said: "Peaches and Thomas are delighted to announce the birth of their son Astala, both were overjoyed at his arrival this week."
Peaches - whose father is Boomtown Rats frontman Bob Geldof - previously revealed she had been due to give birth on April 24, the birthday of her late mother Paula Yates, who died from a drugs overdose in 2000.
She said: "It was amazing for me when they told me that, very emotional and touching and just really beautiful. I was so happy.
"I feel like it’s a little wink from my mum; her way of sending a message to let me know that she’s watching over me and my baby."