Actor and former 30 Rock Star Alec Baldwin and his wife Hilaria have welcomed a baby daughter into the world.

“We are overjoyed to announce the birth of our daughter Carmen Gabriela. She is absolutely perfect. @ABFalecbaldwin @IrelandBBaldwin,” the happy mother tweeted. 

The 29-year-old new mum gave birth to Carmen Gabriela, at Mount Sinai hospital in New York.

Alec's daughter Ireland, from his marriage to Kim Basinger, also tweeted her joy.

”Welcome to the world, Carmen! I'm a f***ing sister!” she wrote.

“I was born October 23. Carmen was born Friday, August 23.”

The 17-year-old model then shared a letter that she wrote for her newborn sister on Tumblr, sharing her own experiences, advice and emphasising the need to walk away from arguments. 

“I love you, Carmen. You have been born into one crazy family”, she wrote. 

“You are both lucky and cursed at the same time. We are going to have so fun much fun together. I can’t wait to meet you soon. I promise you I will always be there for you no matter what!”