The Duke and Duchess of Cambridge have decided to call their son George Alexander Louis, Kensington Palace announced.
The baby will be known as HRH Prince George of Cambridge, as Royal Correspondent Tim Ewart reports.
In a statement, Kensington Palace said:
The Duke and Duchess of Cambridge are delighted to announce that they have named their son George Alexander Louis.
The baby will be known as His Royal Highness Prince George of Cambridge.
The couple are understood to have had a few ideas for names in mind but it took a few days for them to finally confirm which one was right for their son.
It was William and Kate's decision, and all three names picked were chosen because they liked them.
The Queen saw her great-grandson for the first time this morning when she visited the Duke and Duchess at their home at Kensington Palace and would have been told by the couple of their choice.
Historian and biographer Robert Lacey said: "George is obviously a tribute to the Queen's father and will, I imagine, give Her Majesty great pleasure."
George was the bookies favourite boys' name with odds of 2/1.
HRH Prince George is currently third in line to the throne.
Previous Georges who have become Britain's King are:
- George I - ruled August 1714 to June 1727
- George II - ruled June 1727 to October 1760
- George III - ruled October 1760 to January 1820
- George IV - ruled January 1820 to June 1830
- George V - ruled May 1910 to January 1936
- George VI - ruled December 1936 to February 1952
The new prince is currently with the Middleton family in Bucklebury.
William is on two weeks paternity leave and it is expected the couple will enjoy the family support of Michael and Carole Middleton as they adjust to their new role as mum and dad.
A Kensington Palace spokesman said:
This is now private and quiet time for them to get to know their son.