"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," he and Meghan said in a statement on the social media platform Instagram on Wednesday.
Harry and Meghan married in May 2018 in a lavish ceremony at Windsor Castle, west of London, and in May 2019 the couple, known formally as the Duke and Duchess of Sussex, had their first child, a boy they named Archie Harrison Mountbatten-Windsor.
Harry, 35, is currently sixth in line to the throne, and media speculation had been rife that he and Meghan, 38, planned to step back from public life ever since their return this month from a six-week holiday in Canada.
Last year, Harry said he had had disagreements with his older brother, Prince William, who is second in line to the throne, and both Harry and Meghan have had a tense relationship with some British newspapers.
The couple said splitting their time between Britain and North America "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".
This would include the launch of a new charity, Harry and Meghan said, adding that they planned to work to become financially independent.