October 03, 2018 04:35 PM

Kate Hudson‘s mini-me has arrived!

The actress, 39, announced on Instagram Wednesday that she and her boyfriend of over a year, Danny Fujikawa, welcomed their first child, a baby girl named Rani Rose Hudson Fujikawa, on Tuesday, Oct. 2.

“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 in her 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.”

Rani was born at 9:42 p.m. in Los Angeles, according to a birth certificate obtained by The Blast.

Hudson is also mom to 7-year-old son Bingham Hawn from her relationship with ex-fiancé Matt Bellamy and 14-year-old son Ryder Russell from her marriage to ex-husband Chris Robinson.

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Danny Fujikawa and Kate Hudson

RELATED: Kate Hudson and Boyfriend Danny Fujikawa Prepare for Their Baby Girl’s Arrival by Decorating Nursery

In April, Hudson surprised fans and followers when she revealed in a sex-reveal video that she and Fujikawa, 32, were expecting a baby girl.

“[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’s reaction to the pregnancy, “They are very happy. They have been trying to get pregnant.”

RELATED VIDEO: Baby Girl on the Way for Kate Hudson

Since announcing her pregnancy, Hudson has proudly showed off her baby bump on social media, from posing in bikinis to hanging out with Steven Tyler and using beauty products specifically made for expectant moms.

In April, the actress’s brother Wyatt Russell opened 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 how badly 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.”

RELATED GALLERY: She’s Bumpin’ Along! See Pregnant Kate Hudson’s Sweetest Baby Bump Photos

The star recently celebrated her daughter during her summer travels, kicking things off with a European getaway where she hit Greece and Italy with Fujikawa, her sons, her brother (Rio’s dad!) Oliver Hudson, her mother Goldie Hawn and the latter’s longtime love Kurt Russell.

J. Countess/WireImage

“She was excited about traveling to Europe one last time before her baby girl arrives,” a source previously told PEOPLE of the Golden Globe winner.

“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. She is crazy about Danny.”

RELATED: Kate Hudson Jokes That She Needs a “Little Shot of Whiskey” to Help Her Induce Labor

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

Of course, Hudson’s baby-to-be was a hot topic. “Let’s just say you’ve probably never had anyone this pregnant on your show,” she joked, admitting that she and Fujikawa had yet to decide on a name for their daughter but had a list.

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

Kate Hudson's baby shower
Sian Gordon/Instagram

RELATED: Kate Hudson Posts Sweet Bump Selfie with Pregnant Friend, Boasts They’re “Almost There”

Ahead of their daughter’s birth, Hudson and Fujikawa celebrated their little one with a pink-themed baby shower in Los Angeles.

With decorations that included a massive pink-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, including Jennifer Meyer and Sara Foster, who is the stepsister of Fujikawa.

The mother-to-be was dressed in a flowy white crocheted dress and pink flower crown for the festivities, which were put together by friends including Meyer and Foster.

“Grateful for these beauties throwing me the sweetest celebration for baby girl yesterday #WeReady,” Hudson captioned a group photo on Instagram.

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