The Rolling Stones star's son Jesse and the British Tv and radio personality became parents to son Rex in the early hours of Thursday morning (21Feb13).
In a post on her Twitter.com 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."
Wood last became a grandfather in 2009 when his daughter Leah gave birth to a baby girl. Jesse has two sons from his first marriage to Krissy Findlay, while the rocker's stepson, Jaime, also has two kids.
Jesse has previously revealed he plans to marry Cotton, saying last year (12), "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."