Taking to his official Facebook page, Michael posted an adorable snap of Cameron and wife Viviane's little girl, whilst also revealing the baby name that the pair have chosen.
'Congratulations to my son, Cameron, and lovely Viviane, on the birth of their daughter Lua!' he exclaimed in the caption.
Lua Izzy is the first baby for Viviane and Cameron, who is Michael's son from his first marriage to Diandra Luker. The actor, 73, is also dad to son Dylan, 17, and daughter Carys, 14, with second wife Catherine Zeta Jones.
Speaking to PEOPLE magazine, Michael said he was 'ecstatic' about becoming a grandfather.
'Dylan and Carys love being an aunt and uncle and we're so happy to be her Bubba and Zeze,' he said to the title of Lua's arrival.
PEOPLE also revealed that the tot's middle name is a touching tribute to Michael's own father Kirk Douglas, whose real name is Issur Danielovitch, a moniker that is often shortened to Izzy.
In a post on his Instagram account to announce his daughter's birth earlier this week, Cameron said that watching his wife go through pregnancy had left him in awe.
'Today my appreciation for Mother's all over the world has reached new heights...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,' he wrote, accompanied by a photograph of a heavily pregnant Viviane.
Fans have rushed to send the couple messages of congratulations on their bundle of joy, with one writing: 'Wishing you and yours all the best....what a fortunate man you are.'
'Congratulations!! There is no greater gift!!' a second posted, whilst a third said: 'So happy for you. You're going to make wonderful parents.'