UK Prime Minister Boris Johnson says the whole of the United Kingdom will want to wish the Duke and Duchess of Sussex well for the future as they give up royal duties.
It came as the Queen went to church near Sandringham, in her first public appearance since it was announced the couple were giving up their HRH titles.
In her statement yesterday she wished them "a happy and peaceful new life".
But Thomas Markle, Meghan's father, accused them of "cheapening" the royal family.
Earlier this month, Prince Harry and Meghan announced their intention "to step back as 'senior' members of the Royal Family and work to become financially independent".
It prompted intensive discussions between the prince and other senior royals, led by the Queen.
On Saturday, the Queen and Buckingham Palace announced that they had reached a new arrangement - that the couple would no longer use their HRH titles, receive public funds for royal duties or formally represent the Queen from spring.
Speaking briefly to reporters at a summit in Berlin, Johnson said he had been confident the royal family would find a way forward for Prince Harry and Meghan, adding: "I think the whole country will want to join in wishing them the very best for the future."
However in comments made for a forthcoming Channel 5 documentary, Meghan's father, Thomas Markle, accused the couple of "destroying" the royal family which he called "one of the greatest long-living institutions ever".
"Every young girl wants to become a princess and she got that and now she's tossing that away," he said.
"It looks like she's tossing that away for money."
Watch a clip from the BBC interview with Thomas Markle:
Dickie Arbiter, former press secretary to the Queen, said the new arrangement had turned a crisis for the royal family into a "workable situation" that was "the best sort of deal they could have come up with, without totally upsetting the apple cart".
Diana Pearl, a former Royal reporter at People magazine, agreed, saying the perception of the royal family would not ultimately be damaged.
She said the Duke and Duchess of Cambridge "look very solid and drama-free after this whole experience - and they really are the future of the family".
However Katie Nicholl, Vanity Fair royal correspondent, said Harry and Meghan have won their independence, but the royal family has lost their "very magical and unique brand".
Last year, Prince Harry and Meghan spoke of the difficulties of royal life and media scrutiny, with the duke saying he feared his wife would fall victim to "the same powerful forces" that led to his mother's death.
In her statement on Saturday, the Queen said she was pleased that a "constructive and supportive way forward for [her] grandson and his family" had been found.
Buckingham Palace said the duke and duchess understood that under the new arrangement, they were required to withdraw from royal duties, including official military appointments, but would continue to "uphold the values of Her Majesty".
The duke and duchess intend to repay £2.4 million ($NZ4.7m) of taxpayer money used for the refurbishment of Frogmore Cottage, the statement said.
The house in Windsor, for which they will pay rent, will remain their family home as they divide their time between the UK and Canada.
The pair will continue to maintain their private patronages and associations - the duke currently holds 16 patronages, including the Invictus Games Foundation, the Royal Marines and the Rugby Football League; and the duchess four - the National Theatre, the Association of Commonwealth Universities, London-based animal charity Mayhew, and women's charity Smart Works.
They will no longer use HRH, an abbreviation of His/Her Royal Highness, which is part of the title of some members of the Royal Family.
Some questions about the couple's future status remain unanswered, including what their tax and immigration status will be in the UK and Canada.
It is not yet known whether Meghan still intends to gain British citizenship, which would entail her spending a certain amount of time in the UK.
Another question is the issue of their security bill when they are in Canada, said David McClure, an expert on royal finances.
"The Canadians are not keen on picking up the tab, so I'm sure there will be quite heated discussions between the Canadian government and the British government as to who pays for it," he said, adding that the Sussexes might come under pressure to contribute to the cost.
The couple have already begun a transition phase of living in Canada and the UK.
The duchess is in the Commonwealth country with son Archie, where the Sussexes were for six weeks over the festive period.