Sailor joins Liv's son Milo, 10, and David's seven-year-old Gray, the couple's sons from previous marriages.
Liv has spoken in the past about her excitement at adding to her family with sports agent David.
She also admitted being pregnant had made her 'a better mother for Milo'.
She previously said: "The most fun thing about being pregnant is having those mom hormones flowing around.
"You're more present in your body and it's making me a better mother for Milo. You become more like a child. When you're tired, you have to sleep immediately."