Sophie also took to her Instagram Stories to share a gorgeous clip of Jamie toting baby Vinnie in the car seat as they left the hospital.
She revealed her pregnancy news back in October, in a short video announcement which showed Jamie painting the words "Baby boy #3" on a wall inside their house.
Baby Vinnie is the third child, and third son, for Sophie and husband Jamie.
Sophie also admitted her "nesting and cleaning" was "extreme" before her baby boy's arrival, as she packed up all her pre-pregnancy clothes, adding she wouldn't be fitting into them "anytime soon".
Vinnie's two middle names are the name of Sophie's late father Alan, who passed away last year.