The baby girl, named Rani Rose Hudson Fujikawa, is the first for the 39-year-old actress and her boyfriend Danny Fujikawa.
"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," she wrote on Instagram.
"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."
The Almost Famous star revealed her pregnancy news on April 6 via an adorable Instagram video showing the actress screaming with joy after popping huge balloons that revealed the sex of her third baby.
Hudson, who is already a mum to sons Bingham Hawn, 7, and Ryder Russell, 14.