The 36-year-old American actress, who got engaged to the fifth in line to the British throne last month, was extended the invitation as a break from royal tradition, with such an honour usually accorded only to married partners of the Queen's family.
The British monarch traditionally hosts a festive lunch for the 91-year-old monarch's family before leaving for her private Sandringham Estate in Norfolk, where she spends the rest of the Christmas period.
Markle, who is set to marry Prince Harry in Windsor on May 19 next year, has also been invited to join the festivities at Sandringham this year.
Dozens of members of the extended royal family most of whom do not get an invitation to Sandringham gather each year for the family get-together at the London home of the Queen.
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It is believed that it would be the first time for Markle to meet many of Prince Harry's extended family members.
Harry's older brother Prince William also drove his family to the palace in a Range Rover with wife Kate Middleton in the passenger and their childrenPrince George and Princess Charlotte at the back on either side of their Spanish nanny Maria Teresa Turrion Borrallo.
Prince Harry had earlier officially taken over his grandfather's position as Capitan General of the Royal Marines,after the appointment was approved by the Queen.
Harry accompanied Prince Philip, the Duke of Edinburgh, on his final duty as general yesterday as they hosted the incoming and outgoing Commandants General at Buckingham Palace.
The 96-year-old Duke, who had retired from royal duties earlier this year, has been associated with the Royal Marines since 1953, when he was appointed in succession to the Queen's father King George VI.
"The Queen has been pleased to give her formal approval to the appointment of His Royal Highness Prince Henry of Wales as Captain General Royal Marines," a Buckingham Palace statement said.
The Corps of the Royal Marines is at the heart of the Royal Navy's amphibious capability and is considered one of the world's elite commando forces.