May 18, 2016 02:45 PM

And baby makes six!

Soleil Moon Frye and husband Jason Goldberg welcomed their fourth child, son Story, on Monday, May 16 in Los Angeles, she tells PEOPLE exclusively. Born at 5:16 p.m., Story weighed in at 9 lbs., 10 oz. and measured 21½ inches long.

“Welcome to the world our sweet baby boy Story …” the new mom of four, 39, captioned a black-and-white photo of the proud parents cuddling with their newborn.

The actress/author and Goldberg also share daughters Poet Sienna Rose, 10, and Jagger Joseph Blue, 8, and son Lyric Sonny Roads, 2.

“We are a family of unique names. I loved having a name that was different as a kid,” Frye tells PEOPLE exclusively. “We started with our Poet and now our Story feels complete.”

Heather McComb

Courtesy Goldberg Family

Courtesy Goldberg Family

“We are so thrilled about the newest addition to our family. The kids are all so excited and loving their new baby brother,” Frye tells PEOPLE exclusively. “They came to the hospital right after he was born, Lyric jumped up on the bed and said, ‘Cute baby.’ He then gazed at his brother and said, ‘Wow.'”

She adds, “This experience has been truly incredible. We are so grateful and I am cherishing every moment.”

Courtesy Goldberg Family

Courtesy Goldberg Family

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After announcing the pregnancy last year, Frye told PEOPLE that the couple hadn’t planned on growing their brood — but “could not be more excited and thrilled.”

“We were so surprised by this amazing, little miracle…” she shared, adding, “This was definitely a really happy surprise.”

Ahead of Story’s birth, Frye told PEOPLE she was hard at work crafting a unique moniker for her baby boy — somewhat of a tradition in the actress’ family.

“There’s so many crazy, unique names in our household that I gotta really come up with something good, so I’m working on it,” she explained.

No matter the title, the happy family is thrilled that their newest member finally arrived.

“I was not expecting baby number four,” Frye said. “And this was very, very exciting … Jagger was so excited. She was thrilled. I don’t think Roadie really quite understands it yet.”

She added, “I feel like it’s my duty to raise really good people and to try and encourage them to give back and to care and to love others and to be kind. I feel like if I’m gonna have this many kids, I better teach them some really good lessons in life.”

— Lindsay Kimble with reporting by Julie Jordan

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