Amal Clooney has given birth to twins - a girl named Ella and a boy named Alexander.
They were born in London on Tuesday morning, the publicist of her actor husband George Clooney said.
"Ella, Alexander and Amal are all healthy, happy and doing fine," Stan Rosenfield said before joking: "George is sedated and should recover in a few days."
George, 56, married the lawyer, 39, in September 2014 in Venice.
Amal Clooney's parents said they were delighted to welcome their grandchildren.
"They are in great health, all is perfect," Amal's father Ramzi Alamuddin, who lives in Beirut, told AFP news agency.
"I am very happy for them, they will be great parents."
Amal's mother Baria, who is in hospital with her daughter, said: "We are over the moon. It was a beautiful delivery. The babies are beautiful and are doing well."
Other celebrities have congratulated the couple.
Actress Nicole Kidman, speaking at the Glamour Women Of The Year awards in London, said: "Any time a baby is born, I'm like: 'Ahhh'. So two babies it's double 'ahhh'. They have the most joyful journey ahead."
Mia Farrow also added her best wishes, tweeting: "Wishing Ella and Alexander Clooney a warm welcome and every blessing - and congratulations to Amal and George!"
Comedian and TV host Ellen DeGeneres tweeted her best wishes with a reference to George Clooney's Oceans Eleven film franchise: "Welcome to the world, Ella and Alexander Clooney. Congratulations, George and Amal, or as I'm now calling you, Ocean's Four."