March 21, 2015 10:55 AM

Jon Kopaloff/FilmMagic

Jessica Paré‘s happy baby boy is here!

The Mad Men star welcomed her first child, a son, on Thursday, March 19, a source confirms to PEOPLE.

Blues Anthony Paré Kastner is the actress’s first child with her boyfriend, musician John Kastner.

On Friday, Kastner announced their son’s arrival with a sweet Instagram post of his daughter, big sister Summer Lee, 8, holding her baby brother.

The new mom, 34, who stars as Don Draper’s wife on the hit series, managed to keep her pregnancy news under wraps. Her rep confirmed to PEOPLE in October that Paré was pregnant — a month after Kastner announced the exciting news on his Instagram.

Once again, Summer did the honors by posing in a T-shirt reading, “I’m going to be a big sister.”

The final seven episodes of Mad Men will begin airing April 5 on AMC.

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— Anya Leon with reporting by Jennifer Garcia

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