Meghan and Prince Harry had been in Canada over Christmas with baby Archie.
It comes as the Queen, the Prince of Wales and the Duke of Cambridge asked staff to find a workable solution after the couple announced they will step back as senior royals.
The Royal Family was said to be "hurt" at the couple's statement.
Palace sources have told BBC royal correspondent Jonny Dymond that Prince Harry and Meghan did not consult any other royal about making their personal statement.
In their announcement on Wednesday evening, Prince Harry and Meghan revealed they intend "to step back as 'senior' members of the Royal Family, and work to become financially independent".
They plan to split their time between the UK and North America, while "continuing to honour our duty to the Queen, the Commonwealth, and our patronages".
The decision came "after many months of reflection and internal discussions", they added.
On Thursday, BBC royal correspondent Nicholas Witchell said the Queen had been in touch with the Prince of Wales and the Duke of Cambridge.
They all directed senior staff to work with the Sussex household and government to find a solution within days.
It was later confirmed to the BBC that Meghan had left for Canada, said BBC royal correspondent Jonny Dymond.
Our correspondent said Buckingham Palace was "blindsided" by the couple's statement.
There had been talks within the Royal Family about the Sussexes' future - but they were at an early stage, he said.
US President Donald Trump told Fox News he thought the announcement from Harry and Meghan was "sad".
He said: "I don't want to get into the whole thing, I just have such respect for the Queen, it shouldn't be happening to her."
In a statement on Wednesday, Buckingham Palace said: "We understand their desire to take a different approach, but these are complicated issues that will take time to work through."
Despite the couple's decision, Harry will remain sixth in line to the throne.
Last October, Prince Harry and Meghan publicly revealed their struggles under the media spotlight.
After returning to the UK after their six-week break in Canada on Tuesday, Harry, 35, and Meghan, 38, visited Canada's High Commission in London to thank the country for hosting them and said the warmth and hospitality they had received was "unbelievable".
Former actress Meghan, who is American, lived and worked in Toronto during her time starring in the popular US drama Suits, and she has several Canadian friends.
The pair were already preparing to launch their own Sussex Royal charity, which they set up after splitting from the Duke and Duchess of Cambridge's foundation in June last year.
The Sussexes' new charity is expected to be global, linked to Africa and the US, rather than domestic - and will have a commitment to female empowerment.
It was revealed in December the couple had made an application to trademark their Sussex Royal brand across a string of items including books, calendars, clothing, charitable fundraising, education and social care services.
Sentebale, the charity co-founded by Prince Harry, issued a statement saying that, as its patron, he has been a "passionate advocate" for its work, adding: "We know that support will continue."
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