The BBC reported no other member of the royal family was told the statement was about to be released.
In a statement, Buckingham Palace suggested it was trying to talk the pair out of the move.
“Discussions with the Duke and Duchess of Sussex are at an early stage. We understand their desire to take a different approach, but these are complicated issues that will take time to work through.”
The decision is a major blow to the royal family, which is already dealing with the fallout from Prince Andrew’s association with billionaire paedophile Jeffrey Epstein, and will likely be seen as the most serious royal rupture since the abdication of King Edward VIII in 1936.
A new website created by the couple crashed following the release of the statement.
The Duke and Duchess skipped the traditional royal family Christmas at Sandringham and only returned to the United Kingdom from Canada a few days ago.
“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,” they said in the statement.
“This geographic balance will enable us to raise our son with an appreciation for the royal tradition in which he was born, while also providing our family with the space to focus on the next chapter, including the launch of our charitable entity.”
The couple married in May 2018 at Windsor Castle and in May 2019 had their first child, a boy they named Archie Harrison Mountbatten-Windsor.
They have endured intense press scrutiny over recent years, culminating in a decision by the prince to instigate legal action against two newspapers.
“I’ve seen what happens when someone I love is commoditised to the point that they are no longer treated or seen as a real person,” he said at the time. “I lost my mother and now I watch my wife falling victim to the same powerful forces.”
In an interview last year, Harry confirmed rumours of a rift with his brother William, saying the pair were on “different paths”.
The Queen’s son, Prince Andrew, has stepped back from royal duties following a disastrous BBC interview in which he tried to distance himself from Epstein and allegations he was involved in a sex ring.
Bevan Shields is the Europe correspondent for The Sydney Morning Herald and The Age.