The couple were due to travel by train from London to Norfolk on Wednesday but delayed their journey after both coming down with heavy colds.
A day later, they were transported to the estate via an hour-long journey by helicopter.
The monarch and her husband traditionally spend the festive period in Sandringham with their family gathered around them.
In the German tradition, presents are opened on Christmas Eve before a candlelit banquet.
On Christmas morning the family attend the traditional service at St Mary Magdalene on their grounds. On Boxing Day, the Duke of Edinburgh traditionally organises a shoot.
On Tuesday it was announced that the Queen would be stepping down as patron from 25 national organisations at the end of her 90th birthday year, with the patronages passing to other members of the Royal Family.
The move is likely to be seen as a common-sense decision which acknowledges the Queen’s advancing years but Buckingham Palace stressed the monarch is still patron of around 600 organisations.
The Queen and Duke, 95, were surrounded by their family on Tuesday when they hosted their annual Christmas lunch for dozens of relatives at Buckingham Palace.
Despite their advancing years, the couple appear to remain in good health and have missed few official engagements in recent years due to illness.