Kate Hudson ''can't stop smiling'' following the birth of her daughter.

The 39-year-old actress welcomed her first daughter - and first child with boyfriend Danny Fujikawka - into the world last week, and sources have said she's been over the moon with her new arrival, whom she's named Rani Rose.

An insider said: ''[Kate] can't stop smiling. She's always wanted a daughter so this is really a dream come true.''

The 'Almost Famous' actress already has sons Ryder, 14, and Bingham, seven, from previous relationships, and the two boys are ''so excited'' to be big brothers to their sister.

Speaking to People magazine, the source added: ''And her big brothers are so excited - they'll be so protective and sweet to her always.''

Kate announced she had given birth to her baby daughter on her Instagram page.

She wrote: ''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 honor. 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.''

And over the weekend, she shared the first picture of her new arrival, when she took to Instagram to post a snap of Rani wrapped in a blanket fast asleep.

Alongside two rose emojis, she wrote: ''Our little rosebud.''