The actor, 58, shared the news while promoting his latest film The Unbearable Weight of Massive Talent on The Kelly Clarkson Show Thursday.

"I'm gonna announce some big news for everyone," he said. "I am gonna have a little girl."

He went on to share more exciting details about the baby he and wife Riko Shibata are expecting.

"Her name is going to be Lennon Augie, Augie after my father," he added, referring to his late father, August Coppola, who died in 2009. "I'll call her Lenny for short."

"I'm thrilled," Cage said of becoming a girl dad. "It's gonna be the biggest adventure of my life. So, here we go."

PEOPLE exclusively confirmed Cage and Shibata's pregnancy news in January.

"The parents-to-be are elated!" said the rep for the couple at the time.

Nicholas Cage with sons Weston and Kal-El

Jerod Harris/Getty

Last month, Cage said that he and Shibata had already picked out their child's moniker, sharing in the April issue of GQ that they decided on Akira Francesco for a boy and Lennon Augie for a girl.

"Augie was my father's nickname. And my uncle [Francis Ford Coppola] has decided to change his name to Francesco," he shared.

After pulling up an ultrasound on his phone, he added, "I think it's so sweet. It's like a little edamame. A little bean."

This is Cage's third child as he is already dad to sons Kal-El, 16, and Weston, 31, from previous relationships.

The star told Access Hollywood that he is "extremely excited" to be a father again.

"My boys are all grown up, and I miss going to the toy store. I miss singing lullabies and rocking in the rocking chair," he said earlier this month. "I'm looking forward to getting back to that."

Cage and Shibata, his fifth wife, tied the knot during a "very small and intimate wedding at the Wynn Hotel in Las Vegas" on Feb. 16 of last year, a salute to his late father's birthday.

"It's true, and we are very happy," he told PEOPLE in a statement at the time.