Staff have been directed to speed through arrangements for Harry and Meghan to step back from their roles as senior royals.
A Buckingham Palace source said: "The Queen, the Prince of Wales and the Duke of Cambridge have directed their teams to work together at pace with government and The Sussex Household to find workable solutions.
"Expected to take days not weeks."
It has emerged that the Duke and Duchess of Sussex reportedly ignored instructions from the Queen not to go public with their announcement.
The Queen and other members of the Royal Family were said to be "hurt" by Harry and Meghan's decision to issue the personal statement.
The Royal Family is expected to talk to multiple governments over the decision, PA news agency reported, suggesting US and Canadian officials may be involved.
On their new Sussex Royal website, the couple say they are planning to become financially independent as they "value the ability to earn a professional income" - something they are not currently allowed to do.
In the statement issued on Wednesday, they said: "After many months of reflection and internal discussions, we have chosen to make a transition this year in starting to carve out a progressive new role within this institution.
"We intend to step back as 'senior' members of the Royal Family and work to become financially independent, while continuing to fully support Her Majesty the Queen."
This would mean they will no longer be able to use the Sovereign Grant - which funds 5% of their costs - but would still be able to receive income from the Prince of Wales through his private Duchy of Cornwall estate.
The couple plan to continue living at Frogmore Cottage - a four-bedroom property in the grounds of Windsor Castle. The cottage underwent a controversial £2.4m refurbishment at taxpayers' expense last year.
The Grade 2 listed building is owned by the Queen. Harry and Meghan want to continue to use the property as a base while they split their time between the UK and North America.
Reports have claimed the Metropolitan Police, which provides personal protection officers for members of the Royal Family, will review security arrangements for Meghan and Harry.
They are classified as internationally protected people, meaning they receive armed security paid for by the government.
The bombshell statement reveals divisions within the British monarchy which has already been rocked by the Duke of York's disastrous television interview about his relationship with convicted sex offender Jeffrey Epstein.
A YouGov poll on Thursday found that 45% of people supported Harry and Meghan's decision to step back from their roles, while just over a quarter (26%) opposed it.
Nearly two thirds of people (63%) think income from the Duchy of Cornwall for the couple should stop, while just 13% think they should be allowed to keep it.
The poll was of 1,327 people.
Despite their struggles, Harry and Meghan have received several public offerings of support from various celebrities.
Beyonce told them "we love you guys" after meeting them at the European premiere of Disney's The Lion King, alongside her husband, Jay-Z in London in July, 2019.
And after the announcement on Wednesday, Meghan's close friend Jessica Mulroney, a Canadian stylist and TV star, posted a quote attributed to Gina Carey, which said: "A strong woman looks a challenge in the eye and gives it a wink."
But a series of commentators have strongly criticised their decision, with public relations and crisis consultant Mark Borkowski saying about the Sussexes "It does feel like a royal couple in exile".
Harry and Meghan's announcement came on the eve of the Duchess of Cambridge's 38th birthday.
Kate celebrated it with husband William and their children - Prince George, six, Princess Charlotte, four, and 20-month-old Prince Louis.