The Duke and Duchess of Sussex will give up using their Royal Highness titles and return £2.4m to the taxpayer to cover the costs of refurbishing their Windsor home as they leave their roles as senior member of the royal family.

The Queen said in a statement that this “constructive and supportive way forward” would allow the Sussexes “to start building a happy and peaceful new life”. In a rebuff to critics of her granddaughter-in-law, the Queen added that she was “particularly proud of how Meghan has so quickly become one of the family”.

In new arrangements that will take effect from an unspecified date in the spring, the Sussexes will “step back” from royal duties and Harry will not conduct any further official military appointments.

The couple will stop receiving a share of the sovereign grant, the £82.2m that the royal family receives from the Treasury each year. They will, however, remain patrons of various charities and causes, such as the Invictus Games for disabled military veterans created by Harry in 2014.

On 8 January, Harry and Meghan announced, without permission, that they planned to step back from senior roles in the royal family in an effort to become financially independent. The statement came after months of conversations between the couple and their relatives about their unhappiness at raising their eight-month-old son, Archie, in the public spotlight. It led to a royal summit at Sandringham to discuss how to carve out what they described as progressive roles.

The Sussexes expressed their “deepest thanks” to the Queen last night and said they “now plan to balance our time” between the UK and North America.

The Queen’s announcement on Saturday night marked a settlement between the Sussexes and the rest of the royal family about how they will be treated.

The Queen said: “Following many months of conversations and more recent discussions, I am pleased that together we have found a constructive and supportive way forward for my grandson and his family.”

“Harry, Meghan and Archie will always be much-loved members of my family. I recognise the challenges they have experienced as a result of intense scrutiny over the last two years and support their wish for a more independent life.

“I want to thank them for all their dedicated work across this country, the Commonwealth and beyond, and am particularly proud of how Meghan has so quickly become one of the family. It is my whole family’s hope that today’s agreement allows them to start building a happy and peaceful new life.”

Buckingham Palace said that the couple would “no longer use their HRH titles”, but will retain them and Harry will continue to be a prince. This may allow them to return to active royal duties in the future if there is a change of heart.

Much of the public reaction to the Sussexes’ decision has focused on public funding, particularly money spent renovating Frogmore Cottage. This will remain their home but Buckingham Palace said the couple had “shared their wish” to repay the money.

The plan to split their time between the UK and Canada has also caused debate about the cost of public protection. The Metropolitan police spends around £600,000 a year protecting the Sussex family. Buckingham Palace said it would not discuss the new arrangements, saying there were “well-established independent processes to determine the need for publicly funded security”.

The Sussexes issued a statement on Saturday night about the “many months of reflection and internal discussions” that led to their plans.

“We now plan to balance our time between the United Kingdom and North America, continuing to honour our duty to the Queen, the Commonwealth, and our patronages.”

“This geographic balance will enable us to raise our son with an appreciation for the royal tradition into which he was born, while also providing our family with the space to focus on the next chapter, including the launch of our new charitable entity,” they said.

“We look forward to sharing the full details of this exciting next step in due course, as we continue to collaborate with Her Majesty the Queen, the Prince of Wales, the Duke of Cambridge, and all relevant parties. Until then, please accept our deepest thanks for your continued support.”

The Duke and Duchess’ new website, sussexroyal.com, has been updated following the Queen’s statement.