"We are adding a boy to #TeamTrump," Eric Trump wrote on Twitter. "It's been an amazing year. We are blessed!"
The baby boy, the president's ninth grandchild, is due in September.
The couple told People they were still deciding on a name for their son.
"We really loved the name Charlie, but we'd already named our dog that, so it's out," Eric Trump said.
Eric is the third child born to Donald Trump and his first wife, the former model Ivana Trump.
A resident of New York City, Eric serves as a trustee of the Trump Organization along with his brother, Donald Trump Jr.
The president congratulated his son and daughter-in-law on the pregnancy following the announcement.
"Congratulations Eric & Lara. Very proud and happy for the two of you!," he wrote on Twitter.
Congratulations Eric & Lara. Very proud and happy for the two of you! https://t.co/s0T3cTQc40- Donald J. Trump (@realDonaldTrump) March 20, 2017