The couple's first child -- and Trump's fifth -- was born Monday at 8 1/12 pounds and 21 inches, the New York Daily News reported.
The couple chose the name Barron because "they both loved it," a source close to the family told the newspaper. "Donald just always liked the name."
Trump's partner in NBC's "The Apprentice," Mark Burnett, gave the show a plug in his statement congratulating the couple.
"Finally after three years, Donald Trump has a real, true apprentice," Burnett said.