The Queen's great-grandson George was born on July 22 and, talking about the changes a baby brings, the Queen said "... the arrival of a baby gives everyone the chance to contemplate the future with renewed happiness and hope".
During the broadcast, behind-the-scenes footage was shown of the photo shoot at Clarence House that marked the Prince's christening.
The Christmas address is written by the Queen and usually has a strong religious framework, reflects present issues and draws on her own experiences over the past year.
The speech is one of the rare occasions when she does not turn to the Government for advice but is able to voice her own views.
The Queen's traditional message was recorded in Buckingham Palace's blue drawing room.
The room featured a large Christmas tree decorated with coloured baubles, and next to the seated Queen was a table featuring pictures of her immediate family.
The historic picture showing four generations of the royal family, taken at Prince George's christening, was flanked on one side by a black-and-white image of her father, George VI, and on the other by a similar photograph of her mother, the Queen Mother.
The message is available on the Royal Channel on YouTube.
- PA