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The couple welcomed a son named Dakota Song Culkin, after the actor's late sister, Dakota, who died in 2008 at age 29.
The baby was born on April 5 in Los Angeles.
"We're overjoyed," Culkin and Song said in a statement obtained by CNN and first reported by Esquire.
Culkin and Song met a few years ago on the set of "Changeland." They both had roles in the movie.
Culkin is currently filming "American Horror Story" season 10 with Sarah Paulson, Kathy Bates, Billie Lourd, Evan Peters, Lily Rabe and Finn Wittrock.