The singer gave birth to the couple's first child Thursday -- they have named her Willow Sage Hart.
Pink was scheduled for a C-section as the baby was breached and a source tells us the operation went without a hitch and both mother and baby are doing well.
Pink took to her Twitter to announce the good news: "We are ecstatic to welcome our new beautiful healthy happy baby girl, Willow Sage Hart. She's gorgeous, just like her daddy. #beyondblessed." She wrote.