Prince Harry and Meghan Markle promised the Queen that she will hug great-grandchildren Archie and Liliebet "in the near future", during their surprise visit to Windsor Castle yesterday.
According to multiple reports, the secret meeting was "very cordial" and the Sussexes told the Queen she would soon see Archie and Lilibet.
The Mirror quoted sources saying the meeting between the couple and the Queen was "incredibly warm and good natured", while others described it as the Sussexes extending the olive branch to the royal family.
The couple have reportedly re-opened the door to return to the UK for the Queen's Platinum Jubilee celebrations.
The Queen is yet to meet 11-month-old Lilibet, who was named after her childhood nickname.
The meeting between the Duke and Duchess of Sussex and the Queen happened this week, after they flew to Europe to attend the Invictus Games in the Netherlands.
Harry's brother William and wife Kate are said to be skiing in the French Alps with their children.
Royal correspondent Robert Jobson said it was "significant" the couple were not involved in the meeting between Harry and Meghan and other senior royals.
"Hopefully, in time the royal brothers too can break bread and end this new war of the Wales's, which is in danger of turning into one of the fictional soap style dramas Meghan used to star in," Jobson told the Mirrror.
"For William to do that, however, Harry will have to show that he (and his team of PR image gurus and advisers) can keep their counsel at this early and delicate stage. If not, this promising development would all have been for nothing."
Meghan had last seen the Queen at an awkward Commonwealth Day service on March 8, 2020 but the Duchess has previously said they regularly speak on the phone and over video calls.
Harry had not seen his grandmother in person since Prince Philip's funeral last April.