The Queen has agreed a "period of transition" in which the Duke and Duchess of Sussex will spend time in Canada and the UK.
She said she is "entirely supportive" of their desire for a new role but "would have preferred" them to remain full-time working royals.
There is more work to be done but she expects final decisions to be made in the coming days, she said.
Harry and Meghan said on Wednesday they want to step back as senior royals.
In a statement, the Queen said the talks, which also involved the Prince of Wales and the Duke of Cambridge, had been "very constructive".
"My family and I are entirely supportive of Harry and Meghan's desire to create a new life as a young family," she said.
'More independent life'
"Although we would have preferred them to remain full-time working members of the Royal Family, we respect and understand their wish to live a more independent life as a family while remaining a valued part of my family."
She said that it has been agreed that there will be "a period of transition in which the Sussexes will spend time in Canada and the UK" after Harry and Meghan "made clear that they do not want to be reliant on public funds in their new lives".
"These are complex matters for my family to resolve, and there is some more work to be done, but I have asked for final decisions to be reached in the coming days," she said.