On Monday, Michael Douglas' son Cameron Douglas and his girlfriend Viviane Thibes welcomed their first child together - a girl

Add “grandpa” to the list of Michael Douglas‘ roles.

On Monday, Dec. 18, the 73-year-old Wall Street star’s son Cameron Douglas and his girlfriend Viviane Thibes welcomed their first child together — a daughter named Lua Izzy!

“Since Viviane has given birth to a beautiful healthy girl on Monday afternoon, I’ve been at their side ever since,” the new dad tells PEOPLE. “I’m very happy.”

Cameron’s daughter’s middle name is a tribute to her great-grandfather, Kirk Douglas, who was born Issur Danielovitch, and later went by Izzy.

After the birth, the new dad took to Instagram to share his excitement.

“Today my appreciation for [mothers] all over the world has reached new heights … ” Cameron, 39, captioned a photo of a very pregnant Thibes in a yoga pose. “Today I took part in a miracle as my baby girl was introduced to the world through a beautiful Amazon warrior. I’m so proud of you @vivianethibes. 🕊 #iloveyou

PEOPLE confirmed in August that Cameron and Thibes were expecting. “Everyone is thrilled for him,” a source said, adding, “Michael is looking forward to being a grandfather.”

Want all the latest pregnancy and birth announcements, plus celebrity mom blogs? Click here to get those and more in the PEOPLE Babies newsletter.

Cameron’s new arrival comes just 16 months after he was released from prison following a nearly seven-year stay for a drug conviction. In 2010, he was sentenced to five years for possession of heroin and selling methamphetamine. His sentence was extended after he confessed to smuggling drugs into prison.

Viviane Thibes and Cameron Douglas
| Credit: MediaPunch/REX/Shutterstock

Though the troubled times and years behind bars led to distance between Michael and Cameron, the younger Douglas told PEOPLE earlier this month that his family is “closer now than ever.”

“In difficult times, we tend to come closer. It is a beautiful sort of trait that we have,” Cameron said, adding, “My father and I have an amazing relationship. I love spending time with him, and I will spend as much time with him as I can.”

Michael and Cameron Douglas
| Credit: Erik Pendzich/REX/Shutterstock

Ahead of giving birth, Thibes explained the significant role yoga has played in her pregnancy on social media.

“As I come to the end of my pregnancy filled with gratitude for the love and support of my friends and family, I reflect on the importance of regular yoga practice,” she wrote on Instagram.

“Through my practice I was able to find balance and serenity during challenging times. Like a tree, we want to have strong roots in order to stay grounded. So whatever is your source of strength, nourish it because you will need it when things get out of your control.”

Meanwhile, Cameron shared his excitement about becoming a dad earlier this month at the premiere of his stepmother Catherine Zeta-Jones‘ new Lifetime movie, Cocaine Godmother.

“I’m really looking forward to it, and I think it’s going to be more inspiration and drive to really try to put a nice life together for my daughter,” he told Entertainment Tonight, explaining that though he and Thibes were keeping baby names to themselves.

Michael also raved to the CBS show about becoming a grandparent. “I’m going to be a grandfather this month, before the end of the year. I’m very excited. It’s about time,” he said.

  • Reporting by LIZ McNEIL