Meghan and Harry are said to be missing their children, Archie and Lilibet, after spending almost three weeks abroad.
They were in the UK for a charity tour when Queen Elizabeth II died, and the couple opted to extend their trip so they could remain in the country for the funeral.
The Sussexes reportedly stayed at Frogmore Cottage on Monday evening but will now return to their California home immediately.
The royals last saw their children on September 3 – almost three weeks ago.
Prince Harry and a teary-eyed Meghan Markle on Monday
TOBY MELVILLE
Prince Harry and Meghan Markle in Westminster Abbey on Monday
POOL
The report in The Sun comes after Queen Elizabeth II's spectacular state funeral on Monday.
Around a quarter of a million people paid their respects in person by viewing her coffin as it was Lying-In-State.
Culture Secretary Michelle Donelan gave the figure the morning after the nation’s longest-reigning monarch was buried at Windsor Castle.
Ms Donelan said her department was still “crunching the numbers” as to how many people had queued, but that she believed they numbered around 250,000.
She added that most British people would see the cost of Queen Elizabeth II's funeral as “money well spent” but could not put a figure on what that cost might be.
The Royal Family is observing another week of mourning.
King Charles decreed on September 9 that a period of mourning would be observed until seven days after the funeral.
Members of the Royal Family are not expected to carry out official engagements and flags at royal residences will remain at half-mast until 8am after the final day of royal mourning.
They have been consoled by the support and love they have received from the public, including the tens of thousands who turned out to watch the late monarch’s funeral.
Her Majesty was finally laid to rest with her husband, the Duke of Edinburgh, during a private evening burial service attended just by close family.
The family’s website said it was conducted by the Dean of Windsor, adding that Queen Elizabeth II was buried together with Prince Philip at The King George VI Memorial Chapel.