The girls were born Monday afternoon at an Ohio hospital, publicist Simon Halls said. Marion Loretta Elwell Broderick weighed 5 pounds and 11 ounces, and Tabitha Hodge Broderick weighed 6 pounds.
Hodge and Elwell are family names on Parker's side, Halls said.
"The babies are doing beautifully and the entire family is over the moon," Halls said in a statement.
The 44-year-old star of the TV show and film Sex and the City had complained last month to Access Hollywood that the surrogate's telephone and computer had been hacked into, and that the woman had received threats.
Authorities are also investigating whether two Ohio police chiefs burglarized the surrogate's home in the eastern Ohio town of Martins Ferry so they could sell photos and other information to a tabloid.
The burglars were allegedly after "pictures, phone message, all those things" at the home of the surrogate, Michelle Ross, a law enforcement official told The Associated Press last week, speaking on condition of anonymity because no charges had been filed.
A spokeswoman for East Ohio Regional Hospital in Martins Ferry would not comment on reports that the twins were born there.
Parker and Broderick, her 47-year-old husband and fellow actor, had confirmed they were expecting twin daughters by a surrogate. They had been unable to conceive since Parker gave birth to a son, who is now 6.
