February 12, 2015 07:15 PM

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Update: The couple have named their son Sailor Gene Gardner, Tyler announced Friday on Instagram, sharing a photo of her baby boy holding a blue stone necklace featuring a diamond-encrusted anchor.

Originally posted Feb. 12: Liv Tyler is a mom again!

The Leftovers star and her boyfriend, sports manager/agent David Gardner, welcomed a son on Wednesday, Feb. 11, her rep confirms exclusively to PEOPLE.

“He’s healthy and everyone is very happy,” the rep says, although a source tells PEOPLE the baby boy was six weeks early and will need to remain in the hospital for some time.

The baby boy joins big brothers Milo, 10, and Gray, 7, the couple’s children from previous marriages.

Since confirming in September that she was expecting her second child, Tyler, 37, has been posting photos of her growing baby bump on Instagram.

“The most fun thing about being pregnant is having those mom hormones flowing around,” she told Town & Country. “You’re more present in your body, and it’s making me a better mother for Milo.”

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— Michele Corriston with reporting by Julie Jordan

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