The 36-year-old and husband Stephen Belafonte welcomed their first child together at Los Angeles' Cedars Sinai Medical Centre last Thursday.
A source told Radar Online: 'Mel and Madison are home from the hospital. The baby is very loved, and her sisters are absolutely doting on her. Madison is a very happy baby.'
The singer then wrote on Twitter: 'Finally our baby arrives,Stephen nearly passed out,Phoenix screamed, I laughed so hard the baby popped out!!! She is just sooo amazing!! '
The Australian X Factor judge already has two daughters from previous relationships, 12-year-old Phoenix Chi with dancer Jimmy Gulzar, and Angel Iris, four, with funnyman Eddie Murphy.