Kate Hudson’s mini-me has arrived!

“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,” Hudson wrote inher announcement post, which was captioned simply, “She’s here.”

She continued, “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.”

Hudson is also mom to 7-year-old son Bingham Hawn from her relationship with ex-fiancé Matt Bellamy and 14-year-old sonRyder Russellfrom her marriage to ex-husbandChris Robinson.

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Danny Fujikawa and Kate Hudson

“[It] was the most sick first trimester of all my children. Boomerangs have made me nauseous, Superzoom is an easy way to have my head in the toilet, food Instagrams make me [queasy] and thinking too much about Insta stories made me even more exhausted than I already had been,” she captioned the footage.

A source told PEOPLE of the couple’sreaction to the pregnancy, “They are very happy. They have been trying to get pregnant.”

In April, the actress’s brotherWyatt Russellopened up to PEOPLE about his sister’s pregnancy, admitting he got a little emotional when he heard her big news.

“I was happy. I was teary-eyed because I know howbadly she wanted a girl,” he said. “I know Danny, I’m sure in some part of every man’s brain you’re like, ‘I’d love to have a little me.’ "

Added Russell, “But when he met my brother’s little girl Rio, who’s the cutest thing in the entire world, she made him be like, ‘Okay, I want a girl.’ So they’re really excited.”

The star recently celebrated her daughter during her summer travels, kicking things offwith a European getawaywhere she hit Greece and Italy with Fujikawa, her sons, her brother (Rio’s dad!)Oliver Hudson, her motherGoldie Hawnand the latter’s longtime loveKurt Russell.

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“She and Danny are great,” the insider said, adding, “Kate is bubbly with excitement every time she talks about Danny and how they are having a family together. Sheis crazy about Danny.”

On Sept. 20, Hudson appeared alongside her fellow actress mom Hawn, 72, onThe Ellen DeGeneres Show, where she joked that her “water could go any second.”

“We have a couple of them and we’re going to decide when the day comes,” Hudson said.

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With decorations that included a massivepink-and-white flower wall, flower crowns and an assortment of pink balloons, Hudson had a party with many of the couple’s family and friends in attendance, includingJennifer MeyerandSara Foster, who is the stepsister of Fujikawa.

source: people.com