Kate Middleton and Prince William, who welcomed the Royal Baby Monday, issued a statement thanking the hospital for all the facility has done.
The first-time parents said, "We would like to thank the staff at the Lindo Wing and the whole hospital for the tremendous care the three of us have received."
"We know it has been a very busy period for the hospital and we would like to thank everyone - staff, patients and visitors - for their understanding."
A spokesman for Kensington Palace added of the Duke and Duchess of Cambridge, both 31, "Mother, son and father are all doing well this morning."
The couple, who have yet to name their baby boy, will reportedly stay at St. Mary's Hospital until at least 6 p.m. London time, if not until tomorrow.
Hours after Middleton gave birth, William issued a statement of his own. "We could not be happier," the second in line to the British throne said.
The royal baby arrived on Monday, July 22, at 4:24 p.m., weighing 8 lbs., 6 oz. Prince Charles, told the press he is "so thrilled" to be a grandfather.
"Grandparenthood is a unique moment in anyone's life, as countless kind people have told me in recent months, so I am enormously proud," he said. "
We are eagerly looking forward to seeing the baby in the near future."
"He's absolutely beautiful," Kate Middleton's mom Carole told the press upon leaving the hospital. "We are so thrilled. They are both doing really well."
As for the much-discussed Royal Baby name and when we'll learn it, that's anyone's guess ... but you can bet that you will know as soon as we do!