Lourd, star of TV anthology series American Horror Story, had not previously revealed she was expecting.
The 28-year-old announced the surprise news on social media, three months after confirming she was engaged to Austen Rydell.
Alongside a picture of the newborn���s tiny feet, Lourd wrote: “Introducing: Kingston Fisher Lourd Rydell.”
Mark Hamill, Fisher’s Star Wars co-star, was among those congratulating the couple.
He said: “Congratulations to #BillieLourd & #AustenRydell on the arrival of their firstborn child: Kingston Fisher Lord Rydell!!! I can’t think of another baby with both ‘KING’ AND ‘LORD’ in their name. Nice.”
Lourd’s other celebrity friends also shared their well-wishes.
Her Scream Queens co-star Emma Roberts, herself expecting, said: “Screaming!!! Love you guys so much.”
The Lion King star Billy Eichner wrote: “OMGGGGG CONGRATULATIONS!!!!!!!!!!!!”
Unbelievable actress Kaitlyn Dever said: “CONGRATS BILLLIE. IM CRYING.”
And Halloween star Jamie Lee Curtis expressed her surprise at the news and commented: “WAIT WHAT????”
Lourd, who appeared as Lieutenant Connix in the Star Wars sequel trilogy, is the only daughter of talent agent Bryan Lourd and Fisher, who died aged 60 in 2016.
Lourd is Hollywood royalty. Not only is her mother beloved by millions of fans for playing Princess Leia in the Star Wars films, but her grandparents are the Hollywood actress Debbie Reynolds and the singer Eddie Fisher.
With reporting by Press Association