The musician - the oldest son of the late reggae legend Bob Marley and his wife Rita - and his wife Orly Agai Marley welcomed their son Abraham Selassie Robert Nesta Marley into the world on January 26 at a Los Angeles hospital.
According to Ziggy`s representative the baby is healthy and happy and has settled into the family well.
The couple also have two other children, daughter Judah Victoria, five, and son Gideon Robert Nesta, four, while Ziggy has three other kids from a previous relationship.
The 42-year-old reggae artist and Orly - who is a former vice-president of the William Morris Agency, one of the largest talent agencies in the world, and is now his manager - have been married for six years and live in Miami with their children.
His father Bob was responsible for penning such iconic songs as `No Woman, No Cry`, `One Love` and `Redemption Song` and he died in 1981 from skin cancer at the age of 36.