Published Thursday, 21 February 2013
The Rolling Stones star's son Jesse and the TV and radio personality became parents to son Rex in the early hours of Thursday morning.
In a post on her Twitter page, Cotton writes: "Jesse and I are over the moon to announce the arrival of Rex Rayne Wood born on the 21.2.13. Beyond in love."
The new dad added: "Thanks for all your messages about lovely Rex and his mummy! He's fast asleep, so is mum! Over the moon."
Jesse's rocker dad declares: "Love love love little baby Rex... He's such a beautiful little boy. We're so happy for them."
Cotton's celebrity friends also sent their best wishes - former Spice Girls star Emma Bunton gushes: "So excited for Fearne Cotton congratulations and well done mummy!" and The Saturdays singer Rochelle Humes, who is pregnant with her first child, adds: "Congratulations to lovely Fearne Cotton on the birth of her baby boy."
Ronnie Wood last became a grandfather in 2009 when his daughter Leah gave birth to a baby girl. Jesse has two kids from a previous relationship, while the rocker's stepson, Jamie, also has children.
Jesse has previously revealed he plans to marry Cotton, saying last year, "We are definitely going to walk down the aisle. We just haven't decided when. We are living together and I am so excited about the baby."