10/07/2008 at 07:50 PM EDT
Lisa Marie Presley and her husband Michael Lockwood welcomed twin girls on Tuesday, Oct. 7.
"The babies and mom are happy and healthy and resting at home," rep Cindy Guagenti tells PEOPLE.
The baby girls were delivered by C-section at 2:46 p.m. and weighed in at 5 lbs., 15 oz. and 5 lbs., 2 oz.
The singer, 40, had said on her MySpace page
before the babies were born that she and husband Michael Lockwood, 47, were "beyond thrilled and blessed, elated and saturated in happiness."
The girls are the first children together for Presley and Lockwood, a musician. Presley, who proudly displayed her baby bump
in the September issue of Marie Claire
, has daughter Riley, 19, a model, and Benjamin, 15, with ex-husband Danny Keough.
Presley's mother, Priscilla, had confirmed the twins
"She wanted it really to be kept a secret for a long time," the singer's mother, Priscilla Presley, tells Entertainment Tonight
, which broke the news. "And I think women should, because they should be able to announce what they're having and when it's time to make the announcement."
Speculation about Presley's pregnancy first surfaced after a London newspaper published unflattering photographs and alleged that the singer had an unhealthy appetite. Presley sued for libel, and the paper later apologized. She also blogged
about the experience, writing, "I accept their attempt at redemption."
At the time, Presley told PEOPLE,
"Yes, I am swollen. And I am going to gain weight in a city where if you're not a minus size 0, you are fat."
To leave your congratulations for Lisa Marie, visit PEOPLE's Celebrity Baby Blog