The couple's son, Barron William Trump, was born at 5 a.m. and weighed in at 8 1/2 lbs., Trump tells PEOPLE.
"It's a beautiful baby and she's a beautiful mother," says the 59-year-old Apprentice star.
Of his wife Melania, Trump said, "I just think she's looking forward to being a great mother. I have no doubt how good she will be."
The news of the birth was first announced on MSNBC's Imus in the Morning, where Trump did a telephone interview. "I continue to stay young, right? I produce children, I stay young," said the father of five. He already has four children by his two former wives, Ivana and Marla.
Correcting his wife, Donald said: "I expected we were going to have children, so I wasn't totally surprised. But I was surprised by the speed of it. It happened very quickly." (The Trumps were married in a lavish ceremony in Palm Beach on Jan. 22, 2005.)
For the first few months, Melania plans to stay close to home. “But eventually we will take the baby with us," she told PEOPLE. Though she hopes to resume her modeling career, she says she'll be picky about assignments, taking only the ones "that I'm passionate about." Whether she's working or not, Melania has already hired a full-time nanny.