Cruise's fans can't wait to see his daughter's pictures, and use computer to compose a Suri's picture.

The cover of the May 1, 2006 issue of 'People' magazine is shown in this publicity photograph released by People April 19, 2006 featuring actor Tom Cruise and his fiancee actress Katie Holmes detailing the birth of their first child, Suri, as well as photos of actress Gwyneth Paltrow and her new son Moses, and Donald Trump and wife Melania and their new son Barron.

Katie Holmes and Tom Cruise "joyously welcomed the arrival of a baby girl, Suri, today," Cruise's rep said in a statement after PEOPLE first broke the news Tuesday afternoon.

"The child weighed 7 pounds, 7 ounces and was 20 inches in length. Both mother and daughter are doing well."

Suri was born in an L.A.-area hospital – just down the hall from where Brooke Shields gave birth to her daughter Grier on the same day.

The birth went so smoothly that Holmes left the hospital within 24 hours. Holmes, Cruise and baby Suri are back home now and doing well.

Suri "has lots and lots of dark hair and big, blue eyes," says a source close to Holmes's family. "She's going to be a beautiful baby."

Adds Cruise's friend Kirstie Alley: "Tom does everything 150 percent, and fatherhood he does 300 percent. They're going to have a great kid."

The name Suri has its origins in Hebrew meaning "princess," or in Persian meaning "red rose."

Last October, barely six months into their romance, an ecstatic Cruise and Holmes revealed that they were expectant parents.

Cruise, 43, and Holmes, 27, had made no secret of their desire to start a family together: When asked by PEOPLE last June if they were planning to have children, Holmes smiled and said simply, "Yes."

Friends of the Toledo, Ohio-bred Holmes called her perfectly suited to her upcoming role. "She almost seems born for motherhood," said Oliver Hudson, actress Kate Hudson's brother and an old pal who costarred with Holmes in Dawson's Creek. "She's a nurturer. She's got mother qualities a lot of girls her age don't have."

Cruise, meanwhile, is "a great dad already," according to his pal, actress Leah Remini. He has two children from his marriage to Nicole Kidman: Isabella, 13, and Connor, 11, whom Cruise and Kidman adopted as infants. Remini told PEOPLE that both kids are "so cool…You can sit and talk to them about life."