Prime Minister Boris Johnson said the whole country 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.
Speaking at a summit in Berlin, Mr 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.”
The Queen was met by about 100 well-wishers outside St Mary the Virgin Church in Hillington, Norfolk, where she arrived with the Duke of York.
Announcing the decision over the duke and duchess in a statement on Saturday, she said she was “particularly proud” of how quickly Meghan became one of the family and said she, Harry and Archie would always be “much loved”.
The new arrangements, which will begin in the spring, mean the couple will no longer use their HRH titles and will not formally represent the Queen.
HRH, an abbreviation of His/Her Royal Highness, is used as part of the title of some members of the Royal Family.
The duke and duchess will receive no public funds for royal duties and intend to repay £2.4m of taxpayer money used for the refurbishment of Frogmore Cottage.
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.
Prince Harry and Meghan said they wanted to “step back” from their role as senior royals after both speaking about the media scrutiny.
The duchess is suing the Mail on Sunday for publishing what she says was a private letter to her father, raising the prospect of him testifying against her in court.
In comments for a forthcoming Channel 5 documentary, Thomas Markle said the Royal Family is “one of the greatest long-living institutions ever” and accused the couple of “destroying it, they are cheapening it, making it shabby”.
“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.”
The announcement about the couple’s future comes after they held talks with the Queen on Monday.
The Queen said following “many months of conversations and more recent discussions” she was “pleased that together we have found a constructive and supportive way forward for my grandson and his family”.
In its statement, Buckingham Palace said: “The Sussexes will not use their HRH titles as they are no longer working members of the Royal Family.”
BBC royal correspondent Daniela Relph told BBC Radio 5 Live: “When they first issued that statement about what they wanted, (on 8 January) they talked about forging this progressive role within the Royal Family, about stepping back from royal duties. This isn’t stepping back, it’s stepping away entirely.”
She said the question that will “hang over them” for the next year is what their commercial life will look like.
Buckingham Palace said the duke and duchess understood they were required to withdraw from royal duties, including official military appointments.
“While they can no longer formally represent the Queen, the Sussexes have made clear that everything they do will continue to uphold the values of Her Majesty,” it said.
The statement added that the pair would continue to maintain their private patronages and associations.
The Rugby League has said it is delighted Prince Harry would continue as its patron. He held the world cup draw at Buckingham Palace on Thursday.
Rhino Conservation Botswana also welcomed his ongoing support.
‘Harder to think of a much cleaner break’
They will always be, the Queen writes, “much loved members of my family”.
But that’s about it. No royal title, no royal duties, no military appointments, no tours, most of their time spent in Canada, no public money.
It is harder to think of a much cleaner break than this. Harry and Meghan are still members of the Royal Family, but they are effectively no longer royal.
The early talk was of a much more mixed life – one where perhaps Harry and Meghan continued with some royal duties, dividing their time equally between the UK and Canada.
But the contradictions and conflicts of interest were too many.
There are still lots of details to thrash out.
And the whole thing will be reviewed after a year.
But a new life awaits Harry and Meghan – celebrities, certainly, but a different kind of royalty.
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.
While the couple intend to divide their time between the UK and Canada, it is expected that they will spend the majority of their time in Canada.
One question that still needs to be resolved 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.
Blueprint for the future?
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”.
Dickie Arbiter, former press secretary to the Queen, said the new arrangement turns a crisis for the Royal Family into a “workable situation”.
“It’s a win-win situation. It’s the best sort of deal that they could have come up with, without totally upsetting the apple cart – although Harry and Meghan made a pretty good job of that with their bombshell announcement,” he said.
Meghan and Harry have already begun a transition phase of living in Canada and the UK.
The move was agreed by the Queen, Prince of Wales and Duke of Cambridge.
The duchess is in the Commonwealth country with son Archie, where the Sussexes were there for six weeks over the festive period.
On Tuesday she visited a charity in Vancouver which campaigns for teenage girls living in poverty.