Royal baby name rumors are swirling after Kate Middleton gave birth to an heir on July 22, 2013. The pair received their first visitors today, with Middleton's parents Carole and Michael Middleton arriving at the hospital to meet their first grandchild.

Betting sites such as Ladbrokes and William Hill have been swamped with people betting on the future King's name.

Names that have topped the list are George, James, Alexander, Henry and Albert.

Kate Middleton gave birth to a healthy baby boy yesterday at 4:24 PM BST, weighing 8 lbs 16 oz, at the Lindo Wing at St. Mary's Hospital.

The name of the royal baby is expected to be revealed soon, with some speculating that it may be revealed as soon as the couple leaves the hospital today.

A 41-gun salute was held by The King's Troop Royal Horse Artillery at Green Park in London to mark the birth of The Duke and Duchess of Cambridge's child today. The Honourable Artillery Company also fired a 62-gun salute from Gun Wharf at the Tower of London at the same time. The church bells of Westminster Abbey also rang out for three hours.

A spokesman for the Kensington Palace has said, "Mother, son and father are all doing well this morning."

Meanwhile, the new parents released a statement thanking staff at St. Mary's Hospital. "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 during this time."

President Obama congratulated the couple, tweeting: "So pleased to congratulate The Duke and Duchess of Cambridge on the joyous occasion of the birth of their first child."

The royal family released statements on the joyous birth of the Prince, with his father Prince William saying, "We could not be happier."

The palace released a statement saying that the Duchess and the baby are "doing well" and will stay in the hospital overnight.

Clarence House tweeted: "The Queen and Prince Philip are delighted at the news of the birth of The Duke and Duchess of Cambridge's baby."

Prince Charles of Wales also said in a statement: "Both my wife and I are overjoyed at the arrival of my first grandchild. It is an incredibly special moment for William and Catherine and we are so thrilled for them on the birth of their baby boy.

"Grandparenthood is a unique moment in anyone's life, as countless kind people have told me in recent months, so I am enormously proud and happy to be a grandfather for the first time and we are eagerly looking forward to seeing the baby in the near future."

The news of the baby's arrival was first given to the Queen. A bulletin, signed by the Queen's gynaecologist Marcus Setchell, whose team led the delivery of the baby, was taken to Buckingham palace under police escort.

"The Queen, The Duke of Edinburgh, The Prince of Wales, The Duchess of Cornwall, Prince Harry and members of both families have been informed and are delighted with the news," the bulletin said.

Prime Minister David Cameron tweeted: "I'm delighted for the Duke and Duchess now their son has been born. The whole country will celebrate. They'll make wonderful parents."

The Duchess of Cambridge checked into St. Mary's hospital with Prince William at 5:30 a.m. yesterday

The pair arrived by car from Kensington Palace to the Lindo Wing at St. Mary's Hospital .

The royal baby will become third in line to the throne, replacing Prince Harry. He will be given the title Prince and will become the future King of Britain.

"Historically, this is huge," CNN's royal expert, Victoria Arbiter, told Yahoo! Shine. "In 60 or 70 years, this baby will be a monarch. It's also the first time since Queen Victoria that four generations of monarchs will be alive together."

Royal fans have descended onto Buckingham Palace after news of the birth broke.

CLICK HERE to watch the live stream video of Kate Middleton and Prince William's hospital appearance.