The actress gave birth October 2 to a baby girl, she announced on Instagram.
She revealed her daughter’s name is Rani Rose Hudson Fujikawa.
Hudson’s boyfriend, musician Danny Fujikawa, is the baby’s father.
Pronounced ‘Ronnie,’ Hudson said they chose the name to honor the baby’s paternal grandfather, Ron Fujikawa.
‘Ron was the most special man who we all miss dearly,’ Hudson wrote. ‘To name her after him is an honor.’
She added that everyone was ‘doing well and happy as can be.’
Our family thanks you for all the love and blessings that have been sent our way and we send ours right back,” she wrote.
Hudson has two other children from previous relationships.
Ryder Russell Robinson, son of Hudson and Black Crowes frontman Chris Robinson, was born in 2004. Bingham Hawn Bellamy, whose father is Muse frontman Matt Bellamy, was born in 2011.