Kate Hudson is overflowing with affection for her newborn daughter Rani Rose

Kate Hudson is overflowing with affection for her newborn daughter Rani Rose!

Documenting a tender moment shared between mother and child, the actress shared an adorable black-and-white snapshot on Saturday, as she cuddled up with her 2-week-old daughter at home.

Credit: Kate Hudson/Instagram

In the sweet image, Hudson, 39, cradles her baby in her arms while planting a tender kiss on little Rani’s forehead.

“Love is not an emotion, it’s your very existence,” she mused in the photo’s caption.

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Just hours earlier, the new mom let her followers know that even though it had only been two weeks since she’d given birth, she couldn’t wait to start working out again.

“Work out and…pose!” she wrote alongside a throwback photo from a previous gym session, adding the hashtag “CantWaitToGetBackInTheRing.”

Since welcoming her daughter on Oct. 2, Hudson and her boyfriend Danny Fujikawa have been savoring every moment with their baby girl.

Earlier this week the Almost Famous star even shared a sweet photograph of Fujikawa pushing their daughter around in a stroller.

“Strollin,’ ” she fittingly captioned the shot, adding a sun emoji.

Shortly after her daughter’s birth, Hudson — who is also a parent to sons Bingham Hawn, 7, and Ryder Russell, 14 — explained the meaning of Rani’s unique name.

“We have decided to name our daughter Rani (pronounced Ronnie) after her grandfather, Ron Fujikawa,” she wrote on Instagram, referring to Fujikawa’s father Ron, who died in 2012.

“Ron was the most special man who we all miss dearly. To name her after him is an honor,” she added.

Credit: Kate Hudson/Instagram

Danny Fujikawa and daughter Rani Rose

The mother of three “can’t stop smiling” about the latest addition to her family, a source recently told PEOPLE. “She’s always wanted a daughter so this is really a dream come true,” the insider said.

“And her big brothers are so excited — they’ll be so protective and sweet to her always,” the source added of Hudson’s sons.