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In her personal address to the nation, the monarch will pay tribute to the competitors' "skill, dedication, training and teamwork", her office said.
The 86-year-old head of state provided an Olympic highlight when she made a surprise comic turn with James Bond actor Daniel Craig in a short film for the opening ceremony.
"In pursuing their own sporting goals, they gave the rest of us the opportunity to share something of the excitement and drama," she will say, according to advance extracts.
Queen Elizabeth missed a church service at her country retreat on Sunday due to a cold, Buckingham Palace said. Her message was pre-recorded and will go out as expected.
It comes at the end of a landmark year for the royal family.
Queen Elizabeth marked 60 years on the throne with the Diamond Jubilee celebrations and her grandson Prince William and his wife Kate are expecting their first baby.
Prime Minister David Cameron issued his own Christmas message in which he talked of Britain's "extraordinary year".
"We cheered our queen to the rafters with the Jubilee, showed the world what we're made of by staging the most spectacular Olympic and Paralympic Games ever and - let's not forget - punched way above our weight in the medals table," he said.
The first Christmas broadcast was given by Queen Elizabeth's grandfather George V in 1932. It has become a Christmas Day tradition for many families to watch it together after lunch.