Hudson, who is the daughter of Academy Award-winning actress Goldie Hawn, is already a mother to two sons, Ryder Russell, 14, and seven-year-old Bingham Hawn, from previous relationships.
She announced she was pregnant with a baby girl in April.
Hudson later revealed the name (Rani Rose) and said on Instagram: “We have decided to name our daughter Rani (pronounced Ronnie) after her grandfather, Ron Fujikawa.
“Ron was the most special man who we all miss dearly. To name her after him is an honour. Everyone is 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.”